I'm with a credit union, and their sign on the door says NO PETS. However, the policy inside is quite the opposite.
All well behaved pets are welcomed. Kaji always gets attention when we go. If I go without him, the tellers pout. They're awesome! The bank only has 3 branches, and my branch is really far away, making visits sparse. I'm always surprised they remember. Other national banks vary. In ritzier neighborhoods, pets are welcomed. In "the hood" they are not allowed.