If you’re going to be a foreigner in the US, being British is about as easy as it gets, except maybe if you consider Canadians. The prejudice we face is minimal; the most offensive thing someone is likely to say to you is that British food sucks, which it largely does. Otherwise, it’s mostly just a lot of lame jokes: ha ha, did you go to Hogwarts, do you know the Queen, do you guys drink tea like, ALL the time? These are minor annoyances; small things that, in the absence of real problems, appear more significant, but really aren’t.
Having said that: It is suuuuper annoying when Americans pronounce our words wrong. I’m not talking about Edinburgh (it’s Edin-bruh, not Edin-burg) or how you all say Premier League (it’s prem-ee-er, not prum’eer, and no one calls it EPL). I’m talking about the perhaps most important word we have: twat.