How to avoid supervisors with prejudiced views?

I will sound snarky with this answer, but have you tried talking to them?

Your question may ask well be asked as "How do I determine the values of another human being before I meet them?" And I would say that is not something you can truly learn and understand until you talk with them.

You may respond with, 'What if they lie?' And that's a very valid point. But I would tell you that all of human social interaction is this very problem, and that you will not gain the wisdom of how to interact with humans without interacting with them!

I recently heard that a good question to ask is “What do you think that others [perhaps other scientists] think about ...” The idea is that most bigots think their bigotry is pretty normal and their beliefs are widely held in secret. So they might tell you that “other people” think X and you can update your beliefs accordingly, unless they follow this up with a convincing argument about why they think most people are wrong. This method is certainly not conclusive, but it can provide a way to start a conversation or a give a bit of extra evidence one way or the other.

How can a prospective student identify these people and avoid them?

You are playing a very dangerous game here. Are you going to make your little test public? If yes, won't the bigots quickly learn how to game it and intentionally avoid detection (as they apparently are doing now according to the premise of your question)? But I am actually more concerned about the opposite option, that you will apply a secret purity test and brand people as bigots or not according to your own private criteria. This can lead to two sorts of problems:

• False negatives. Some people (maybe the more clever or sophisticated among the bigots) will still figure out what your game is and manage to avoid being detected. You're back to where you are now, except with more of an (incorrect) expectation that you know who's a bigot and who's not. Not so good.

... and then there's the much worse:

• False positives: your private test (that I assume you intend to share with a select group of people who will be the "users" of the test's results) will invariably "flag" some people as bigots who are just... normal people.^* Of course, those people will not know that they have been flagged or why, and will have no means to defend themselves. You will damage their careers, probably their reputations, and at the end of the day, what will you achieve? You have denied someone who is likely a perfectly good advisor and mentor to the students who need one, who are exactly the people you are trying to benefit.

^{* I personally know two well-respected male academics who were recently accused of sexist behavior by women at their universities, leading to both men suffering a great amount of anxiety and fear of career damage before having their name cleared after pointless (and very stupidly handled) investigations by their university administrations. I have heard first-hand descriptions of both incidents (which occurred independently to two people who don't even know each other) and am 99% confident that they were blown completely out of proportion. So if you think these sorts of mistakes don't happen, think again.}

To summarize: the idea that you can somehow figure out a way to look deep into people's hearts and decide if they are good or bad according to some value system is appealing in its simplicity. But we've been there before. For your own and others' sake, my suggestion is: don't.