My approach is to choose a strategy (i.e. what actions to take, given what I know and possibly in future situations where I learn more), based on an expected-value estimate, and let my emotions follow.  Emotions that affect actions have a few use cases: (1) as a shortcut, (2) behaving "irrationally" for game theory purposes (e.g. gratitude, pride, loyalty, etc. making you trustworthy to others; anger and vengeance discouraging others from mistreating you), (3) motivating you to do something that you intellectually know is the right thing.

In the football coach case... Exactly what actions are you deciding between?  If you imagine yourself as one of the team owners, then I imagine you'd want to consult more carefully with some experts, then confront the coach with some arguments (possibly bringing a trusted expert along), demand he explain himself, and see how satisfied you are with his explanation and planned future actions, and decide based on that (plus other considerations) whether you want to do something like get a new coach.

But if you imagine yourself as you... what are you going to do?  Email the owners?  Email a sports journalist to try to get them to research the issue and make a stronger case in public?  Complain to other fans at parties?  (Just for fun, or because you hope the idea will spread and eventually bubble up to the owners?)  I suspect pondering the actions you might take would help you clarify your emotions: maybe "Eh, it annoys and disappoints me, and I will note it as a likely instance of high-level incompetence and will mention it in relevant discussions, but I'm not bothered enough to do more than that"; or "Yes, I am seriously offended by the idea that my team is being run by a bozo, and I will start contacting people about it, and maybe do some more research to strengthen my case."

I guess the inchoate anger you describe may be taken as a signal that you need to think out the situation and your strategic options.

(Incidentally, I think that, for many news items, the chain of questions "What are you going to do about it?" → "What emotions does it make sense to have about it?" → "What is the point of your even knowing about it?" is a good one to follow, with a conclusion many news purveyors do not want you to reach.  (It is possible for random news items to be useful in unexpected ways, but, well, should it bother you that you haven't read the majority of the 13 million articles from the NYT alone?  Of course not.  So you should only bother collecting news items that seem likely to be useful, or if you have some purpose in mind.))

For the FDA case: For the record, my position is that the FDA appears to be a bunch of bureaucratic jerks who would rather delay a lifesaving drug and watch 10,000 people die, than approve a bad drug and watch 10 people die; that they've been like this for decades, and that this is presumably due to incentives they are for some reason faced with.  Historically this hasn't ranked very highly among my list of complaints about destructive U.S. government interventions, but now it's more relevant and important and obvious, and I have some hopes that the issue may get addressed.

Now, in terms of actions?  I'm not a politician, nor do I know any, nor do I think they'd listen to me; nor do I have a communications platform better than arguing on internet forums; among people I know, generally they either agree with me already or seem unlikely to respond well to my injecting my politics into a conversation.  So I think what I'll do is make the point about this most obvious failure of the FDA when COVID policy comes up in conversation, and otherwise just remember it.  (If I were in charge of a political organization, then I guess I could do something.)

For the Stallings case: Ok, so, if you personally had any prospects of running into the guy, then you might or might not decide he has bad judgment.  The legal case itself is decided, unless you think you can influence an appeal.  What is the point in having emotions about it, or even in knowing about it?  What actions does it help you with?  You could use it to judge the people who decide to talk about it—although if you yourself are confused, then what conclusions could you draw from the positions others take?  (I guess it's possible to say "This argument contradicts itself/makes non-sequiturs and appeals to emotion, so I can note that its author is untrustworthy" independently of the underlying issue, but you could do that without even knowing the facts.  Knowing the facts helps only with detecting people who make well-formed arguments from false premises.)

To me, the main application is the legal-theory and rules-of-engagement angle—essentially the exercise of figuring out for yourself what the rules should be, and then also judging our current legal system and society based on how they agree/disagree with you, and seeing if there's anything you want to do about any difference you find.

Object-level look at Stallings: If someone is being aggressively shot at, and gets hit, is it reasonable to expect him to stop and take the time to think "Hmm, I think that hit less hard than a bullet is supposed to hit—maybe these are rubber bullets", before deciding to self-defensively shoot back?  I'm not sure if people think that's supposed to be a reasonable expectation, but one thing the article mentions is that it's an official policy that rubber bullets should be fired from orange-barrelled guns to mark their non-lethality, and that the officers violated this policy.  I think I'm inclined toward the position "If you want to aggressively shoot at people with nonlethal bullets and expect (in a legal sense) them to not shoot back with real bullets, then the burden is on you to do everything to signal that your bullets are nonlethal; if you miss one of the signals that a reasonable person is supposed to check for, then they are within their rights to shoot back and kill you."

It seems there might be another position: "If the police are shooting at you, you're never justified in shooting back in self-defense, no matter how aggressive and unjustified their actions might be, because they're police."  I dislike this position—I prefer the position that the police have no special rights or immunity that ordinary citizens lack.  Nevertheless, even if we accepted it: since you do have the right to self-defense against non-police, it follows that there must be rules about whether the citizen can be reasonably expected to know that those shooting at him are police.  I would be inclined toward a similar position: "If the police want to aggressively shoot at people and expect (in a legal sense) them to not shoot back, then the burden is on the police to do everything to signal that they are in fact police; if they miss one of the reasonable-person signals, then they can't complain about being shot."  According to the article, the police wore SWAT uniforms but came from an unmarked van—I don't know if anyone has a list of reasonable-person "We're police" signals, but I'd accept that one—and Stallings says he in fact didn't know they were police, and dropped his gun and lay down when he realized.

I suspect that at least one of these legal-theory angles would have been discussed in the trial, if I checked it.  ... Hmm...

Reading the document at the bottom (it's labeled "body camera transcript", but is actually a judge's order), going through the judge's "findings of fact", the following things strike me as important: (a) the officers were inside the van when they were shooting and when Stallings shot back; (b) it was dark (past 10 pm), and it says "no interior lights are activated, except for those on the dashboard"; (c) I'll just quote this whole section: "None of the officers in Unit 1281 announce their presence as law enforcement nor did the van have its lights or sirens activated. Neither Officer Stetson nor Officer Cushenbery wait to determine whether Mr. Stallings posed a threat before shooting at him. Officers Stetson and Cushenbery testified it was dark and Mr. Stallings was approximately 70 feet away when they shoot from the moving van; that testimony is credible and is supported by the video evidence"; (d) "The officers immediately yell “shots fired, shots fired” and rush out of the van. Mr. Stallings says it was only then he realized the occupants were law enforcement. This is credible since he is seen immediately placing his rifle on the ground, away from his body[...]".

The document has some irritating stuff where it seems there is indeed a law providing special protection to police officers, and that the application of that law doesn't require that the defendant know that the officer was an officer (but that different jurisdictions have different rules)... But it also says this, in its explanation of why the judge is allowing Stallings to claim self-defense:

Minnesota law authorizes the use of reasonable force toward another when a person reasonably believes they are resisting an offense against that person. The Minnesota Supreme Court has recognized defendants have the right to resist an “unjustified bodily attack” from law enforcement. This has since been referred to as self-defense. Deadly force, however, is not permissible against police officers “who have announced their presence and are performing official duties." [...] It would seem, therefore, defendants may use deadly force in self-defense against an unjustified bodily attack from law enforcement who have failed to announce their presence."

Here, Unit 1281 failed to announce its presence. Indeed, it appears the team deliberately wanted to not be identified in advance as law enforcement. The unmarked van had no distinctive exterior (law enforcement) lights or signage. The van did not use its siren. The interior lights, except the dashboard, were off. And the officers wore all-black uniforms at night. Additionally, against MPD policy, all officers in Unit 1281 were equipped with black-barreled 40mm launchers. The white, unmarked conversion van was followed by marked squad cars flanking its rear right and left sides. However, the flanking squad cars were not immediately behind Unit 1281’s unmarked van. Finally, Unit 1281 never verbally warned or announced their presence before Officers Stetson and Cushenbery fired their 40mm launchers at Mr. Stallings. Because Unit 1281 did not announce its presence, Mr. Stallings may claim self-defense if he satisfies the elements for the defense[...]

Ok, this seems like a relatively reasonable rule—not exactly the position I stated above, but acceptable—and in this case leads to a good outcome.

The article also says the police kicked and punched Stallings when he was on the ground, then lied that he resisted arrest and ran away (body camera footage proving the lie).  The judge's writeup confirms this. ... I think any officer who does that should be charged with a crime and/or fired.  Article says "As of Thursday, there are no updates on whether any discipline will be handed down to officers involved in this incident."

By the way, it's often the case that, if P is true, then actions A+B+C are best; and if P is false, then actions D+E+F are best; but if P seems to have e.g. a 50% chance of being true, the best strategy is neither A+B+C nor D+E+F, but rather A+C+F+G.  It seems like this gets lost in some mainstream discussion.

For example, if someone is suspected, possibly accused, of some kind of misconduct, but strong evidence has not been put forth and an investigation won't yield results for a few weeks, then perhaps your estimate of his guilt is somewhere in the 20-80% range.  In that case, punishment is probably inappropriate (there is a common legal principle that "It is better that ten guilty persons escape than that one innocent suffer", which may be interpreted to mean "Punishing an innocent is at least 10x worse than letting a criminal escape, and therefore you shouldn't punish if your guiltiness likelihood estimate is less than 90%"), but doing nothing may be suboptimal.  There are usually precautions and remedies you could take in the meantime, where the "benefit if you're right" is much higher than the "cost if you're wrong".

If the misconduct is some kind of harassment or other mistreatment of those around the suspect, then an obvious precaution is "make him take a vacation for a few weeks while the investigation proceeds" (i.e. administrative leave), while remedies would include offering time off and free counseling and other support to those who claim to have been mistreated; the costs are fixed and low, and the benefits if guilty seem high.  If it's academic fraud, then I imagine worthwhile precautions include bringing in a competent third party to double-check his work on any current and not-yet-published studies (delaying their publication if necessary), and remedies include requesting replication of past studies whose results anyone cared about (this should happen more often in any case).

There's been rhetoric around issues of this kind that makes me think the discussants can't effectively work with any probability estimates other than 0% and 100%; either the alleged perpetrators should be locked up, or the alleged victims should be ridiculed, and everyone needs to make up their minds right now; a notion like "The probability is high enough that we should offer comfort to the alleged victims, but low enough that we shouldn't end the alleged perpetrators' careers, and should wait for more evidence from a serious investigation" seems outside the conversation.  Duncan's Split and Commit post made a related point.