That you think they're going super hard woke (especially Disney) is perhaps telling of your own biases. 

Lets look at Disney and Hollywood (universities are their own weird thing). The reality is that in the Anglosphere there are lots of progressive people with money to spend on media. You can sell "woke" media to those people, and lots of it. Even more so when there's controversy and you can get naive lefties to believe paying money to the megacorp to watch a mainstream show is a way to somehow strike back against the mean right-wingers. And to progressive people it doesn't feel like "being lectured to about politics", because that's not what media with a political/values message you agree with feels like. So going woke is 100% a profit-motivated decision. The leadership at big media companies didn't change much over the last decade or two, nor likely did their opinions (whatever those actually are). But after gay marriage gained significantly above 50% approval rate in the US and the Obergefell decision happened it became clear to them that it was safe to be at least somewhat socially progressive on issues like that, and would be profitable.

But equally, almost every single "woke" Disney movie has the "woke" components carefully contained such that they can easily be excised for markets where they are a problem. You see a gay kiss in the background of a scene in Star Wars, it gets cut for the Chinese and Middle East markets. Disney has many very progressive employees who are responsible for making the actual art they produce; artists lean pretty strongly progressive in my experience, so of course the employees' values come out in the art they make. But the management puts very strict limits on what they can do precisely because anything less milquetoast is believed to be less profitable.

You're thinking at the wrong level of abstraction. There is no economic incentive for wokism at the corporate level. But look one level below. The question isn't what causes "corporations" to act in woke ways. The question is, what persuades employees of corporations to act in woke ways?

My hypothesis is that anti-discrimination legislation has, due to court precedents, developed an inverted burden of proof. If a corporation fires or disciplines someone who is non-white, female, disabled, or belongs to a number of other protected categories, it is now up to the corporation to prove that the firing or discipline was done for non-discriminatory reasons. This, combined with the ideological leanings of most people in HR departments, is sufficient to ensure that every corporation has, within it, the equivalent of an ideological cell, whose job it is solely to push the corporation to act in a more woke manner. This ideological cell has both public opinion and federal law on its side; well meaning individuals who push back end up like James Damore.

But unless this had profit appeal I would expect the market to just… eat pure but incomplete ideological capture after a while

The market is part of society. There was a similar argument made against anti-segregation legislation in the 1960s. After all, given that it's more profitable to sell to both black people and white people than it is to sell to white people only, wouldn't it be in business owners' rational self-interest to desegregate their properties?

The answer, in both instances, is the same: if there is a sufficiently high cultural barrier, then it will be more profitable to go with the culture than against it. Most reasonable people can at least nod along to the woke slogans. After all, it is quite reasonable to suggest that women ought to be treated equally to men, that blacks should be treated equally to whites, and people shouldn't be discriminated against because of their sexual orientation. It's only when those reasonable propositions are taken to extremes that they result in wokism.

Because of this motte-and-bailey aspect to wokism, it's easy for wokism to permeate the culture, and for advocates of wokism to tar those who oppose them as racists and bigots.

But there’s a counter-push of “Lots of people don’t like being lectured about politics when they’re seeking entertainment” (for instance). It’s not at all clear to me that the first effect is so utterly hugely enormously larger than the second that the profit incentive would cause so many companies to swing hard woke.

Lots of people also threatened to move to Canada if Trump was elected President. How many of them actually chose to do so? A Republican in the United States will shout vociferously about Coca Cola or Nike engaging in woke behavior, but will he or she choose Pepsi when he or she next shops for groceries? Will he or she buy some other brand of shoes? And if he or she does, will it make a difference? After all, Pepsi and Reebok are hardly less woke than Coca Cola and Nike.

Random theory I heard: When Disney releases a new black princess, the fact that toxoplasma of rage forms around it provides them a lot of free advertising. Most people are like 'shrug' and don't care that much, but the fact that everyone's complaining and/or hyping it gets it onto most people's radar.

One possible incentive for corporations to promote wokism is that it's a distraction from other forms of activism which might their hurt bottom lines more. 

Also as Bryan Caplan and other comments pointed out, regulations may also drive this shift: the regulations leave companies vulnerable to lawsuits with vague criteria and a defense strategy is to 1. not be the slowest target (this results in a race/escalation) and 2. prepare a vague signaling defense (look at all these employee training programs we do, surely that proves your vague and non-falsifiable accusations of discrimination must be wrong).

A large part of it is the US legal system and anti-discrimination law playing out in counterintuitive ways. The key think is that where corporations are concerned, US law runs on counterfactual court cases; the actual text of legislation matters only insofar as it affects those court cases. Combine this with management having imperfect control over employees within a corporation, imperfect resolution of facts, and a system for assigning damages that's highly subjective, and executives are left in an odd position.

Every company which does a significant amount of hiring and firing, ie every company above a certain size, will fire and reject some number of people in protected groups. Some of those people will claim that it was because of their group membership, and sue. As a distant corporate executive, you can't prevent this, and can't tell whether the accusation is true.

But you can put everyone through some corporate training. And it seems that the empirical result, discovered by legal departments that have been through this many times, is that you get the best outcomes in the court cases if you go over the top and do reverse-discrimination that the letter of the law says should be illegal.

If you think of "wokeism" as a luxury belief - something that many people like to use to show themselves as virtuous, but don't really do a cost/benefit of any component of behavior or signalling, this makes more sense.  Also, don't confuse yourself into thinking systems or corporations have beliefs or intents.  They are merely aggregates of diverse actors who happen to be near each other and have intertwined behaviors.

Signaling of wokeism is pretty rampant in today's youth, who are the biggest customers and large part of the workforce for the things you mention.  It's probably not ideologically attractive to the elites or leaders, but it's not obviously harmful, so they're better off supporting (or at least accepting) it than dealing with massive conflict within their orgs and among their customers.

Off the top of my head (and slightly worried that this will become a major culture war thing, but I will answer the question that was asked):

• There is a principal-agent problem.  If pursuing wokeness comes at the expense of profits, the latter doesn't necessarily affect the people who make those decisions very much.
• My impression is that many of the executives are in fact woke, and others are at least unwilling to say otherwise.
  • Wokeness seems pretty optimized for shouting down and intimidating opposition.  (I think much of the specifics of the ideology were and are determined by some people successfully shouting down others within the woke movement.)
• At least in the entertainment industries, when a distinctly woke thing is made, there tends to be a narrative that evil people hate the thing, and therefore anyone who hates the thing is evil, and therefore lost profits should be treated with an attitude of "good riddance" rather than "maybe this thing was made badly".  I think this tends to be the woke narrative, and generally promoted by media—and, as per the previous item, any opposing narrative would tend to get shouted down.

From my experiences at a very woke company, I tend to agree with the top comments here that it's mostly a bottom-up phenomenon. There is a segment of the employees who are fanatically woke, and they have a few advantages that make it hard for anyone to oppose them. Basically:

• They care more about promoting wokeness than their opponents do about combating it, and
• It is safer from a reputational standpoint to be too woke than not woke enough.

Then we get a feedback loop where victories for wokism strengthen these advantages, leading to more victories.

The deeper question is whether there is also a system of organized top-down pressure running in parallel to this. Elon's purchase of Twitter presents an interesting case study. It seemed to trigger an immune response from several external sources. Nonprofit organizations emerged from the woodwork to pressure advertisers to leave the platform, and revenue fell sharply. Apparently this happened before Elon even adjusted any policies, on the mere suspicion that he would fail to meet woke standards. 

At the same time, there was a barrage of negative media coverage of Elon, uncovering sexual assault scandals and bad business practices from throughout his life. Perhaps a similar fate awaits any top-level executive who does not steer his company in a woke direction?

I'll end with an excerpt from an old podcast that has stuck with me:

It is impossible to defend the idea that the invisible hand of the market would guide them [corporations] to this course of action. I’ve been inside a large company when it was adjacent to this kind of voluntary action — where corporations all act in lock step — you’ll just have to trust me here — and I’ve seen the way it’s coordinated.

What will happen is a prominent journalist or several will reach out to the company’s leadership team and ask them for a comment on the current thing. Especially they do this if  that company has any history of dealings with the object of the cancellation or the scandal.

The influence of these kinds of journalists, from publications such as the New York Times or the Atlantic, is such that even their most innocuous question is a threat; no threat is ever stated, but all parties involved understand the discussion. Once a few highly visible players perform the designated action, all the smaller players get in line.

They have the nerve to call this a preference cascade, when in reality it’s an obedience cascade.

Money is an inventive, not the only one. People also want to be seen as socially acceptable. not reviled Pariahs.

The simplest explanation to me is that most of the things one would call "woke" in media are actually pretty popular and accepted in the culture. I suspect most people don't care, and of the few who do more like it than dislike it.

It seems strange to me to be confused by a company's behavior since you'd normally expect them to follow the profit motive, without even mentioning the possibility that the profit motive is, indeed, exactly what is motivating the behavior.

What tendencies specifically would you classify as "woke"? Having an intentionally diverse cast? Progressive messaging? Other things? And which of these tendencies do you think would alienate a significant portion of the consumer base, and why?

Edit: I've changed my mind a bit on this on reflection. I don't think the purpose is appealing to the few people who care, I think it's about stirring up controversy.

As far as running a media company goes, fandom is extremely profitable, increasingly so in an age where enormous sci-fi/fantasy franchises drive everything. And there's been huge overlap between fandom communities and social justice politics for a long time.

It's definitely in Disney's interest to appeal to Marvel superfans who write fanfiction and cosplay and buy tons of merchandise, and those people tend to also be supporters of social justice politics.

Like, nothing is being forced on this audience -- there are large numbers of people who get sincerely excited when a new character is introduced that gives representation for the first time to a new minority group, or something like that.

As with so many businesses, the superfans are worth quite a few normies who might be put off by this. I think this is the main explanation.

deleted due to excessive downvotes.

"Woke" is a pejorative neologism for "rights-and-equality-respecting" coined by the anti-equality/human-rights/anti-LGBT/racist crowd. (Edit: Sorry, actually not coined by them.) What is called "woke" is actually normal, and what they'd call "normal" would have to be sanitized to avoid offending their sensibilities (white main characters, non-LGBT couples, etc.).

My guess as to why "woke" (actually normal) culture is marketable is that the anti-rights-crowd is both getting smaller and losing its marketing power.

(In the future, when not wanting to signal the allegiance to the Bad Guys crowd (to both them and normal people), avoid using the word "woke" and find some other way of expressing the same sentiment. Example: "I can't understand why is there a gay couple in a new movie. Any idea why they put such a bizarre, not-related-to-reality and not-appealing-to-viewers thing there?")