Well, we have two alumni in the car in my family... But, to me, that just means you are part of a the school's alumni. It's pretty standard when you're part of a group. I mean, LeBron James doesn't wear a jersey with "CAVALIER" on the front.
This is tortured logic. In the one case you are advertising a team mascot, in the other your are talking about yourself. Yes, I wear t-shirts that say OHIO BOBCATS. You wouldn't catch me dead in a t-shirt that said OHIO ALUMNI. I'm not plural, though some people have thought that I was a little psycho. However, I'm no Billy Milligan.