I don't see why we shouldn't take them seriously. A person is a person. Some people are eccentric or they go through phases of self discovery that don't appear to make sense of others.
I think the polite thing would be to just ask the person. How do you identify? And then treat them according to their answer. I don't see why you also couldn't just ask about the inconsistent presentation in a tactful way.
Maybe they aren't MtF, but an androgyne. Someone who mixes up their gender expression. If that is true, however, I would suggest they use the men's room. I understand how difficult it is for some people to accept the concept of androgyne and, it's pretty obvious the idea of a 'man' in a women's room makes women uncomfortable.
I guess I'm saying if the plumbing matches what the beard represents, the person should defer to tradition. In a case such as this. Usually, I'd say let them do whatever, but, let's face it, public restrooms are separate for a reason.