Ah. Gotcha. I thought you meant you don't leash your dog in public. My bad.
I still think the restaurant thing is kind of silly (I'm not a fan of the trend toward treating dogs like people), but it sounds like you're more the "I have my dog with me" type than the whiny asshats I've encountered who insist their animal has a right to be there. The former are generally cool, they latter not so much. Regardless, it's certainly the property owner's right to choose whether they want dogs.