Is that sort of thing legal, in the US? Or is it more like, it's illegal but everybody does it anyway?

I live in the UK, in the EU. Here, it's illegal to ask candidates questions about their race, religion, age, marital status, family planning etc. As it is illlegal to advertise jobs to "white male 30 yrs old" etc.

Of course, people still do stuff like that- e.g. I've been asked about my age a couple of times and apparently it's common to be asked about whether you're planning to have children soon, by interviewers, though this has never happened to me (so it might depend on the industry).

I don’t think the UK is very different from the US in this respect. Discrimination based on race, religion, etc is illegal. Asking race, religion, etc as part of the application process is not illegal. Actually, they are supossed to do it (while preventing those details from influencing the hiring process).

The point is that there is a lot of people who do care about race, not just US cops.

https://race.bitc.org.uk/sites/default/files/kcfinder/files/...