Given that the OP is asking about a flight "a few years ago," I assume it predated September 11, 2001. Whether there was ever a Minnesota law prohibiting that airlines request ID - I don't know. There is no such law in effect right now, in MN or any other state.

As everyone else has pointed out, photo ID does NOT equal security. It equals pretend security or an illusion of security, but doesn't equal real security.

That said, flyers in MN are not exempt from the general requirement to show photo ID to fly. As others have said, of course, failure to show ID just gets you the "you must be the terrorist we've been looking for" treatment.