The ones in resort towns seem to always have “no foreigners” signs in English…I guess to avoid having any awkward denials at all. Seems perfectly legal to not serve foreigners, in any case.

I get away with it by saying I'm Hafu, and then asking if it's for me. Once you ask, and you are fluent in Japanese enough, they don't care.

This is not to say there is no racism in Japan, but for resorts it's most likely they don't have the capacity to help in English/Foreign Language.

If it's some seedy thing, like a cheap/seedy bar, karaoke, J/KTV or sexual services then it's both, no English and they want discretion.

I haven't really seen many of those signs in Tokyo. I could imagine that in resort towns they want to keep tourists out? Having tourists who don't understand what those places is asking for trouble I guess.

I’m sure the snack bars cater to Japanese tourists, these are resort towns and the snack bars line the main tourist streets. But the fact that they also attract a few foreign tourists (because we also enjoy onsens) they need the signs.