Where's PrincessMimiChica?? She can answer this question far better than I can, but I'll try...
There are certain fans to every show, like you have your people obsessed with Les Miz, or Cats, or Wicked, or any other show. RENT is just like those shows- some people (like me) think it's amazing, and they would like to see it 40, 50, or 1000 (like Joel) times because they love it so much.
I don't see anything wrong with obsessing over it. Like NYCBabe said, "I'd rather be obsessed with RENT than Eminem", which is totally true. Where all my friends are "obsessing" over Jessica Simpson and Nick Lachey, I guess I would say I "obsess" with RENT, because it's my favorite show and everything. But have I seen it 40 times and own all the merchandise? No, but I still think I'm a bit obsessed.
I have my books and my poetry to protect me...