They aren't invading the privacy here.
Yes they are, they're forcing you to disable Private Relay.
They are preventing a malicious actor from running an attack via VPN and ssh tunneling in addition to IP address, device, etc.
This makes no sense. I could walk outside the store and do any of those things on my 5G connection. Private Relay does not enable these attacks and blocking it doesn't prevent them.
At worst they are associating IP with browsing at competing stores.
Wut? They are the ones assigning IP addresses. Not sure what you mean.
At worst, they're using your IP address to join your walmart.com session cookie with complete time series data on your store position, data from store cameras, etc. to build a creepy profile without consent.
Preventing the VPN was likely required by a lawyer and auditor and a risky attack vector for a billion dollar company.
It's not a problem for Starbucks. As long as the public facing network is separate from the internal store network, e.g. with a VLAN, what is the concern?
If Walmart was breaking https and inserting man in the middle games it would be in their policy.
Regardless, it would be shitty behavior.
If they were cracking crypto schemes and were decrypting your traffic, it's entirely possible this violates a "hacking" law in the US.
Other commentators went off into fantasy land edge cases where traffic is being decrypted. And it still doesn't change my expectation of privacy on a public hotspot.
It was a hypothetical to explore the extent of your "their house, their rules" viewpoint.
And that's why you should use tools instead of trying to blow a house down if you wanna eat some little pigs.