I mean most stores here are pet friendly. The only ones that aren't are grocery stores and restaurants but even then i have seen people with small dogs in a carrier. In the grocery store one time i saw a guy with a pom in one of those carriers that go on your chest. It wasn't enclosed or anything and the pom was sticking out and nobody said anything to him. I haven't tried it there. But i did take one of the girls to Fairway in their carriers, but they weren't peeking out and the bag was closed so no one even knew. I've taken them to all kinds of stores and the mall too and all went good
I think its fine as long as you're either carrying them in a carrier or something.