"Is [it common for shops to disallow entry of customer bags & packs], or do the majority allow you in with packs?
In my experience, quite a lot of big name chain grocery stores in Spain disallow entry of any and all customer bags, packs, and shopping trolleys, but they provide a convenient self-serve lock-up facility just inside the door. The lock-up facility varies between coin-deposit-operated lockers and coin-deposit-operated permanently-tethered chains that are fitted with a sort of plug that goes into a locking socket, to form a bag-securing loop. The usage-enablement key remains captive until a coin is deposited, but the same coin is returned later when one re-inserts and turns the correctly-numbered key to retrieve one's bag. The system is extremely straightforward, intuitive, and easy to use.
Smaller family-run shops tend to have less formalized security requirements, but there are practicalities: some of them have narrow aisles, which introduces the risk of a wearer of a backpack inadvertently knocking merchandise off of the shelves that are behind the pack-wearer, and/or bumping into other customers. I have unwisely entered such a tightly-spaced shop while wearing my backpack, and then realized that I needed to find an aisle intersection where there was more space, so that I could carefully remove my pack and carry it outside, lock it up, and then re-start my shopping.
BTW that is why I keep my chain and padlock in an easily-accessible outer pocket of the pack.