There's always going to be issues with the terms because both any termd chosen will fail to capture both the internal and external perspectives. Toxicity, for example, only shows how a certain type of manhood effects people who come in contact with it. However, a young man searching to be an adult in the world may come across this way of being a man and doesn't necessarily see it as a good fit. So it's too "rigid". I'm not sure we'd want to talk about one's "rigid manhood" but the quality is notable. We could also use the term "The Man Box" to capture the difficulty of people who struggle to meet these impossible standards.

I also like the term hyper-masculity, but there are worthwhile questions there too.

It's important that remember that no term will do a great job of capture the full range of issues facing society and men, but even a cursory investigation will show how different vantage points help show and counter balance different terms.

For white privledge, we have to remember that in this society the baseline or default is white, male, young, affluent, etc. These people don't get that suspicious look or assumption that they aren't capable or criminal or dishonest like the OP noted. We could say society has minimal friction for them.

So as to not just have some more noise, here are some of my dumb suggestions: white tailwind, white standard, white default, white baseline, presumed while white.