I think you'll find snobs and weirdos on both sides.
Most cats are of the "domestic shorthair" variety and people don't even know that's a distinct breed, it's just "cat". But God forbid you call one of the exotic breeds a "trash goblin", the owner will chew your face off.
Likewise dogs. One neighbourhood lady is still not speaking to me since I mispronounced the breed of her hair monster, but most dogs around are "dunno, might be some labrador in there" and similar.
And there's one other owner who refused to admit the dog's breed, telling everyone who asked it was a mutt, because "it's a difficult breed and [he] didn't want people to get one just because it's fluffy".
There's all sots.