I'm the same way, always take my pups in a carrier to the vet to keep them safe. It's one of my pet peeves, people who don't control their dogs in the waiting room. Sometimes it's a big dog, with a small kid holding the leash, and not in control.
As far as stupid rude comments, I had Kayla and Karlee both in one carrier, and a guy said "what have you got in there..... oh a couple of ankle biters", and I just responded yeh and they are really vicious.
Some people are just plain ignorant and stuff rolls out of their mouth without any thought. You can't fix stupid, so I've heard.
So I don't let it get to me.