Well, they do help in identifying people committing crimes with surveillance cameras. I’ve been asked to remove hats and back packs at stores and have seen no hoodie signs for this very reason.
Though none of those things are the same as religious garments, so I am not suggesting they should be held to the same standard.
I do contend though that I think covering one’s face IS culturally significant. Unless there is a good reason for it (really cold, skiing, dust mask, germ mask etc), someone masked makes people uncomfortable. Part of this is popular culture and real life criminals and terrorists using masks or hiding faces to do bad things. There is also a primal thing because facial expressions do a LOT of silent communicating. Masked faces make it much more difficult to determine if someone is friendly or not. If 3 guys came into a store with bandanas or their shirts pulled up, wouldn’t that send you some alert signals?
Now don’t mistake this with condoning the manager’s actions. Obviously religious garb such as this, even if uncommon, should be familiar enough for one to override their uncontrollable reactions. And most likely Islamophobia played a big part.
My point is that for most people hidden faces have a psychological impact that one can’t fully control, and have to consciously override. Remember it wasn’t that long ago we wore war masks and paint and that was done for a reason (faces are special).