Unless we're at a petstore, Billi is always in my purse and I've managed to take her in plenty of stores (even a couple restaurants) without anyone saying anything. Most people don't mind her in the purse, since she isn't touching anything. I think one store asked me to put her in the bag all the way (I have the Jaraden, where she can hang out a little if she wants to) and no biggie, I just popped her in and closed the opening on her.
I was allowed (actually, requested) to take her out and let her run around at Hancock fabrics in my town tho. They got a kick out of her.