But the thing is that it is not that terrible. If someone distrust me or keeps their distance because they are afraid of me, it is their right. I don't think it is fair to expect them to "get over it" just so I can avoid feeling "falsely accused".
On the other hand, people judge all the time for multiple reasons. What is worse, that sexist men accuse me of being a slut, or having achieved something sleeping with a boss just because they wanted that and are angry because I manage to do whatever and they don't or that a black men thinks that I have benefit from racism? I'm giving you a hint, it is more likely that the second is true, even if it wasn't intentional or my doing.
Example: Once I was looking to rent. The owner of the apartment thought that a white woman who went to the same school as her was more trusworthy than other people wanting the same thing. If there was a black men wanting to rent the same place (unlikely but possible), I had an edge. On the other hand, I've never had sex with a boss or even a coworker.
Whenever someone accuse me of something, it is worth considering where did they come from. Why are they accusing me? They might be partially right even if I've done nothing.
Women are afraid of men because they have been raised to be afraid of men. Specially strangers and the more different, the more suspect. It takes time to change how you have been raised. And if when you are trying to analyze your prejudices you happen to have experiences that make you afraid, you risk confirmation bias.
The fact is that both white and black men can be nice, but they can also be pushy or scary or many things. In doubt, you take the "safest" approach. In the same way that I won't blame you for doing what you can to avoid misunderstanding and false accusations or racist white women, I think it is normal that women do things to be as safe as possible. After all, if we are raped or assaulted, we are going to be blamed.
If it is any consolation, what makes me mistrust someone is certain actions. Like ignoring "no" or invading my space without reason. Or some "dog whistles". And yes, I apply the same to women. When you analyze (or in my case overanalyze XD) things, bulling, harashment, sexual abuse and other terrible things share paterns. And also overlap. A racist person is usually also sexist and homophobes. So if I detect someone who is homophobe, automatically asume is not to be trusted. I might not openly say it or confront the person, but I do react to that.
But people rarely agree with my take on things. You can see it here. You think that by "showing me" that being "falsely accused" stings I would stop distrusting or holding accountable. The way I see it is the other way around. It is fair to be accused and forced to think if there is truth because otherwise I might be doing things that are wrong. Not on purpose, but doing them anyway.
In this case, if I walk a lone street at night and I said that I feel scared because I crossed paths with a black man, then I might be giving "reasons" to some racist white men to be violent with such black man. Notice that here, how I feel is valid and true. But it is a third who twist that into "he was a danger" and could scalate into something I've never wanted. I mean, you have arrived, you are safe, nothing happened and you don't want the black men to be attacked. Well, knowing that my words can be twisted, I might be more careful on what I say to avoid giving excuses for violence.
Turn it around. Some of your words or actions might affect me in ways you don't want to. For example, at a bar, commenting that I'm slutty among your friends, might seem minor, but you might be signaling to a third man that it is ok to grab my ass. After all "all women are whores", right? No big deal. And once it is ok to grab my ass or crots or tits, is it really so much worse to rape me? Well, they won't call it rape, they would call it sex and claim that while I've never said yes, I really wanted it and "actually, I must enjoyed it". It is the same discourse. The people who do those things is just wanting an excuse, a social pass to do shitty things.
So I rather be falsely accused and deal with the sting because otherwise, yes, we are giving them a "pass" or a convinient excuse even if that wasn't our intention. After all, if you don't tell me, I would remain confortabily oblivious to the consequences of my initial, not in bad faith, comment about "feeling unsafe".
