I think the analogy is closer to "refusing service to those who refuse the rectal thermometer test upon entry to a store".

I see the analogy but there’s a pretty big difference between hiding your face and hiding your device’s IP address. The former is a social norm going back tens of thousands of years, the latter is an arbitrary and artificial artefact of man made technology in the last 30.

A better analogy is sending mail with either proxy return addresses or none at all. Both are socially acceptable in most circumstances.

Why a store would ban a balaclava if the person fully authenticates himself and has a long good track record and does nothing wrong?