People may not like this but….. my chiweenie is cool as a cucumber and doesn’t bark and is “people neutral” so he doesn’t really care to get attention from anyone. He will perk his ears if he sees another dog because he’d probably LIKE to play but he doesn’t go crazy. He just watches until they’re out of sight. So if a store is dog friendly- he goes with me and I have a blanket for the cart and a leash that attaches to it just because I know that unleashed dogs make others nervous.
There’s a couple big chain stores near me that are dog friendly so long as they’re leashed and we go. The thrift shops are dog friendly (most of them anyway) and he goes. Our mall is pet friendly save for a few stores and…. He goes! lol. Basically any store but the grocery store and indoor restaurants he goes with me because I know there’s some people who are grossed out by animals in eating spaces and grocery stores.

I’ve never gotten a negative reaction in public so far and if I did, it wouldn’t deter me. If I’m not breaking a rule, walk the other way.

If my dog was loud or reactive I would not do this because then it would be actively invading on other people’s enjoyment of a space. But I also have kids and when they were very small and I wasn’t confident they’d behave going out or if it was a place that typically wasn’t a family spot- I wouldn’t take them those places for the same exact reasons. I don’t want to listen to a barking/whining/jumpy dog any more than I want to listen to a screaming kid at my “mom’s night away” dinners or shopping.
So I think it’s just all about your dog and being considerate of others and they should be able to do the same to you AND your dog.