I'm not sure why you're being downvoted. This is a thing that happens. Usually because the cashier hasn't been trained.

These days I don't generally need to ask because the terminal have very conspicuous Apple Pay logos on them. But sometimes the terminal is kept behind the counter, so you can't see.

I've had several occasions (most recently at my vet) where I was told that it wouldn't work and I said, "Let's try it anyway," and it worked just fine.

Yes, I’ve had this happen and usually I just assent and pull out a card. Since I’ve just asked to avoid feeling rude, I’m probably not going to try Apple Pay in defiance of them.

When I’ve thought Apple Pay would have actually worked in that kind of situation, I try it next time I’m there (without asking first!)

In my experience, some small businesses avoid Apple Pay/Google Pay because you can add American Express cards to them, and they want to not accept Amex cards in order to save on the fee, despite the service agreement of their payment processor obligating them to.