I don't know what the laws are and I'm not sure if they would even apply to a small, private group like AA where the members of the group decide what the rules are. It might be like private clubs where they can even ban certain people...which is horrid, but I think that's a thing. I know my parents belonged to a country club which until fairly recent history was allowed to ban certain races. Yes, true. Now they can't outwardly ban, but they can just simply not allow membership. Its pretty horrid. And those are humans, not dogs.
I love dogs and the meetings I go to allow them. I know that they ask that no one pet the dogs during meetings because I think some folks get irritated by the distraction. Its similar to children. They are cute as heck and everyone wants to ooo and ah. I could care less but I know it irritates some people. So a lot of meetings don't allow children. Which can be really hard for single addict Moms for sure.
If you can, find a more accepting meeting. If not, try not to let it bother you. The ones that are pissy about the dog would probably be harassing you if he were a kid too. Whatever!