Banks, to my knowledge, are privately-owned businesses. They should be allowed to ask for any type of security-related identification as they see fit.
If you don't like it, carry it.
It's when the government starts to act like a privately-owned business that bothers me.
And I think the government does act like a privately owned business, with unjust taxes, compulsory education, mandatory insurance, etc.
But that's another thread.