I want very much to visit Budapest, but I've also been hearing a lot about the political climate under the current government, which seems hostile to foreigners and ethnic minorities. Is it safe to visit Hungary if you are Arab, Jewish, black, Latino, Asian, etc., etc.?
I guess by "political climate" you mean the government's communication.
The hostile communication definitely dropped after the elections. Second, it mostly only took root in the poorer parts of the countryside. So would you visit a poor village in Hungary as an ethnic person, you may get some hostile looks, but that's the worst even there. If you visited only Budapest, then you would be as safe as any other tourist.
I live in Budapest, and even though I'm Hungarian myself, I see ethnic people every day, and none of them gets attacked or anything.