Being serious about security means evaluating whether a small inconvenience can lead to catching more perpetrators, and therefore recovering more funds. It logically follows that clothing and accessories that cover the face in any way are going to be a problem in recognizing and catching criminals, so I don't see how this qualifies as security theater as you seem to be implying.

Your toupee/wig example is reductio ad absurdum, so I won't bother to respond to it. There are obviously problematic corner cases like religiously-mandated head coverings, and I think the policies on those need to be clarified, but I really don't see the massive infringement upon liberty of asking customers not to wear anything that can cover their face during a covert bank robbery. Focusing on this tiny inconvenience when banks are doing so many worse things on a daily basis is missing the forest for the trees.