I think the real issue here is what the obligation is to find out more so a more individualized decision can be made, and the answer here isn't necessarily the same for civilians and police.

For police, because we invest them with the power to do a great deal of harm when it's called for, we want to make especially sure that they only use the most justifiable criteria for deploying their powers. As a society, if our police are so starved for resources that a cessation of racial profiling would result in, say, a substantial increase in the murder rate, then our obligation as members of society should be to try to increase police funding to meet our ideals, not accept the profiling.

However, for individuals, the degree of positive obligation we can impose on them to the detriment of their own safety is very limited, and the ability they have to gather additional contextual information to make a better risk assessment is also very limited. If they have a particular consistent risk threshold, then I don't think we have any business telling them they must raise their risk specifically for the benefit of some other racial group. If they are wrong in their assessment of risk--the airplane example--then of course we should call them out for that. But a society that imposes levels of risk on its members that its members do not find acceptable is not a good society. Our goal there should be to change the facts of who is more likely to pose a danger, not behavior of those correctly reacting to the danger. We then should help those communities from which a large amount of criminal behavior is arising to have better job prospects, better education, better policing, etc..

One big problem--or at least an arguable problem--with your reasoning is that you're defaulting to a group-level morality rather than an individual morality. Sometimes that's warranted, but it deserves a detailed argument.

Let me illustrate the problem.

Suppose Dude-Bro is a good guy, but he looks kind of sketchy. Some people avoid Dude-Bro because people who look like him are dangerous like 3% of the time, and that's more than they care for. Not fair, Dude-Bro hates that. He's pained by the insult. But tough luck, Dude-Bro. Teed isn't coming to your rescue.

Suppose Bro-Dude is a good guy too, but some people avoid Bro-Dude too because, again, people who look like him are dangerous like 3% of the time. Bro-Dude hates that. He's pained too. But wait, there's hope! Teed's here to help!

This is a pretty crap deal for Dude-Bro. Bro-Dude and Dude-Bro have the exact same situation of getting shunned not because of who they are but because what people correctly infer about someone-who-looks-like-them. But you come to the aid of Bro-Dude and not to the aid of Dude-Bro because Bro-Dude is black and Dude-Bro is white. That sounds kinda like racial prejudice, doesn't it?

More argument is needed to explain why this is not just permissible (instead of immoral) but in fact morally superior. Sometimes I see such arguments, but you didn't make one here.