Is it a “lot of people?” Growing up as a brown guy in the south I’d think about my ethnicity maybe once a month? If that?
I assume there’s a spectrum, but I also think the public view is very distorted by who gets amplified. You can’t get tenure or get your op-ed published in the NYT writing about how being a minority in the US is fine and people are pretty nice.
I'm not sure spreading the problem to everyone else is very good solution.
That in itself is a stereotype. Ask the people you know who fit your description if they feel like they have to put up a facade or keep up their guard. Let’s see how prevalent that is.
So if anything, maybe having to be on your guard all the time will help people learn what it is like to be a minority and can then understand why it is helpful to at least be somewhat thoughtful in how you treat people of diverse race/gender/cultural background.