The local Wal-Marts around here won't let you bring a messenger bag, backpack, daypack, panniers, seatbag, or handlebar bag into the store with you. I tried to walk in once with my daypack on my back and was told to leave it by the carts. When I got back to pick it up the employee was nowhere to be found and my daypack was laying there unattended. Wal-Mart is sexist, you can carry a 10 gallon purse into the store, you can carry a diaper bag into the store, but you can't (as a man) carry any bag into the store. And you can't leave your stuff anywhere secure.
If I'm going to go to Wal-Mart then I drive the car. I like walmart, but I don't and won't bicycle there.
As to the drive-thru banking, I heard once the argument was that it was an insurance liability issue, same as if you walked up to the drive-in lane. That argument sort of dies when you ride up on a motorcycle.