I don't see why a backpack is any different than bringing your own bag. Anyway, probably what I'd do is bring a reusable or thin canvas bag in my knapsack and secure the knapsack to the bike when I went in the store. However, I don't know how secure you'd be doing that. I've never had a problem leaving bags with customer service, either. It's a drag, though.
I don't know that I'd call it discrimination but it sure isn't customer-friendly to bicyclists. When I shop on the way home, I have my wallet in my backpack, which means I'd have to carry it in my hand while shopping at Pete's. I'd worry about misplacing it that way. I've never had a problem at any of the stores I shop in. Maybe a note to the manager would be helpful?
It's not discrimination. It's the lack of adding a "provision" for cyclists, assuming they enforce the rule equally for everyone. Yeah, make a suggestion to the management, I bet they change the policy.
"More prone to theft" is not enough justification to you? (assuming it's true, of course)