Let's just suppose that there is an actual, proper, clear study (or more than one) showing that a no-hat policy does reduce the rate of robberies in banks by 10%. Would you then agree with a no-hat policy? I would.
Let's instead suppose that the study shows that such policy would reduce robbery rate by 0.001%. Would you then agree? I most likely would not, after investigating what an inconvenience that is for customers (or, better, how inconvenient they perceive/consider such policy).
Let's suppose finally that such policy was instituted just because the security director thought "hey, I want to see people's face, so you'll see they'll stop robbing us!"... Then I would not agree, and consider that bank run by at least one idiot. Probably more.

All three scenarios above are possible, to me.

None of the above has anything to do with being rude or polite. I would not want to use a bank where personnel is rude. It did happen to me in the past and it was one big reason, albeit not the main one, to change bank.

I see no matter of principle in this no-hat policy, but rather balancing pros and cons. I don't even see an infringement upon freedom. A no-hat policy does not particularly touch ethical, moral, religious values, in most cases (and when it does I agree with Tony C that that should be clarified). Asking to be naked in a bank is in no way similar to wearing no hat. Nudity has moral, ethical, religious implications for 99.9% of customers in the Western world, and possibly all over the world. No-had is just like no-phones. If the benefit is tangible, measured, real, then it can be easily assessed whether the policy makes sense or not.

Mostly, I find in this case that the bank did a very poor job in communicating to the customers, and treating them with the very due respect. Signs everywhere, politeness, and even apologizing for the inconvenience, together with an explanation of what the benefits are and how that is all done for the sake of everyone's safety, would have been much more effective.