Suppose you're an intellectual, and other people in your civilization are Doing Something Wrong. Normally this isn't a (unique) problem. You can explain how housing policy is flawed over and over in the hopes someone else does something about it. 

Occasionally, however, civilizations are Doing Something Wrong because they've taken incorrect beliefs and absolutely run wild with them. Think Christianity during the middle ages. Large numbers of people adopted a silly core idea - in this case that the Bible is an accurate, literal historical record - and used that to justify entire paradigms worth of political and social institutions. 

By the time intellectuals had caught their bearings, simply suggesting that society no longer spend money on elaborate churches wasn't an option. Christianity had become a uniquely resilient meme, in part because it was a self-policing ideology that produced acolytes. 

Acolytes become bad news for the intellectuals in three steps:

1. First, one or more large (and false) propositions are made that provide solid foundation for an ideology, a basket of social reforms justified by the Big Lie(s). 
   
   Most misconceptions are insufficient tinder for ideologies. An incorrect belief about plumbing doesn't justify a Department for the Correctness of Plumbing, and more importantly isn't very memetic outside of some plumbing association. 
   
   On the other hand, if you're a first century peasant who believes in the holy origins of Jesus, you've got a lot of work to do. He provides a casus belli for you to be very opinionated about how others ought to change, and a books' worth of a material for your critiques.
2. Convinced of this misconception, a critical mass of revolutionaries embark on a quest to reshape their clans, communities, and nations according to that ideology. Because their demands are so far-reaching (and because all social movements are secretly pyramid schemes), they usually end up asking to command new social or political institutions.
   
   If the revolutionaries succeed, a fraction of them become installed into religious or government leadership. This creates a new class of governors who believe full-throatedly in the Big Lie, whose status rests on continued compliance with and belief in the ideology, and who have the go-ahead to force that compliance. 
3. Finally, the newly installed acolytes produce a self-reinforcing justification for viciously defending its Big Lie from critique. Often, such as for Communism, inquisitors are legitimized simply on the basis that dropping the ideology would lead to social changes that are, according to the ideology, Really Bad. 
   
   Other times, it's because the ideologies' designers literally hardcode those justifications. Middle ages Christianity states that entry to heaven is conditional on believing in God while you're on Earth. Social justice activists assert that anti-minority words and thoughts themselves are the root source of outcome differences. In either cases the ideology is self-reinforcing, because the more people that believe it, the more acolytes there are to object to criticism on the grounds that the ideology forbids criticism. 

If this process is successful enough, an ideology reaches "escape velocity", which happens when the revolutionaries have seized enough social and political capital to make criticizing the most dubious pillars of their doctrine Against The Rules.^[1] 

You generally want to stop ideologies before they reach escape velocity, not after. The thing that makes ideologies so terrible at this point is that most of their conclusions, taking the Big Lie as a given, are fairly sensible. If the Bible really happened, and people get tortured forever if they don't follow its prescriptions, then it's hard to argue with spending lots of money on churches and executioners. By plugging up the original flaw in their rhetoric, Acolytes can maintain their mandate to reshape society, even if everything they want to do is ultimately batshit insane and costs 50% of GDP. 

As someone who doesn't believe in the Big Lie, your instinct will be to argue with this initial lie anyways. But that's hard. In certain cases arguing the root belief may even really be so controversial, at least in the environment the acolytes have engineered, that this would backfire entirely.

There is a compromise: join the reformists.

The reformists may or may not agree with your atheism. If they do, they don't claim so in public. The reformists are instead most visibly concerned with the excesses of the acolytes, the public works and stonings that would seem most shocking to an unindoctrinated observer. Their rhetoric tends to have a flavor of reductio ad absurdum. 

"Obviously we should let people trade a little, right?"
"Obviously we shouldn't put gay people in prison, right?"
"Obviously these "woke" people are crazy, right?"

These arguments are pretty lame. Reformist ideology doesn't make a whole lot of sense, frankly. If you really agreed with the premises, why wouldn't you agree with the conclusion? But clever and quick-witted reformists can find contradictions in acolyte ideology, they can dispute that A implies B, and they can seek out secondary sources that show acolyte policies don't produce the effects they promise - all without directly attacking the core pillars of the ideology, which would mean social or political consequences.

It's a delicate dance. Acolytes, sensing danger to their equilibrium of dissent-punishing, will try to prove that reformists are actually atheists so they can strip them of their authority, or worse. Often the acolytes are right - the reformists are heretics - but reformists try to sit on the edge of what's socially acceptable so that acolytes can't establish common knowledge. The effectiveness of the tactic thus greatly depends on the political acumen of the reformist. They'd be at a strong disadvantage if they weren't ultimately right.

Though maybe you're not interested in compromise. You see through the Big Lie. Perhaps you don't have the social skills to make it as a moderate, or you're too honest or self-righteous to bend the knee to power.

There is another path; become an atheist:

You might look around and wonder why people ever become atheists, aside from pride or a sense of honor. They always lose!

Well, not always. Sometimes they dramatically overturn the existing order. Usually, however, they don't, especially when you consider the unfamous ones. In many cases it's obvious to everyone from the beginning that they won't succeed in even causing much of a visible shift in public opinion. So, what gives?

One (optimistic) answer is that our measure of success is flawed. You shouldn't measure the atheist by the number of fellow atheists they create. Most people are just unwilling to become outspoken atheists, no matter how convinced they are that the Big Lie isn't true. 

Instead, measure the atheist by the number of reformists they create. The atheists' long, well-needled statistical or rhetorical critiques of the existing order won't be virulently memetic, and they will complain about them not winning the battle directly. But for everyone that becomes an open heretic, a hundred or more read their words, notice their correctness, and go into their businesses and government bureaucracies knowing something new. There's reasons why the "woke!" objection, an inane comment that doesn't mean anything, can get so popular in the first place. It's certainly not the acolytes that are passing that bark along. 

1. ^{^}

   To be clear: the degree to which these rules are enforced by ideologues varies in an extremely significant way. Usually it depends on how strong a society's deontological commitment to truth and civil liberties is. Communism is one of the nastiest historical examples.