> Does it really matter if that cute girl at the check-out is an anti-Semite?

This matters rather a lot if you're Jewish. You're arguing that "it doesn't matter if you don't look up", Star Wars passim.

Similarly it matters if your hairdresser is an anti-vaccer and spreads something contagious to you.

A certain amount of difference can be looked past, but when it comes to matters of life and death - and it can come to that surprisingly easily when things get heated - it matters.