I think one of the biggest keys to this whole thread is learning how to read body language. If I hang just to see a star come out, I usually just smile and compliment them and then stay the heck away. I don't move in, just play it by sight. They are tired, have to catch the train and god only knows what might have happened to them that day. (One time, an actress in a show I went to see had a death in the family that very day and still went on, god love her.) You simply never know what's going on inside their minds.
As for the whole stage door thing, well...it's a catch twenty-two. Being a stage door loser is part of the process of LIVE theater and I think most actors are being silly if you think that door is going to be empty when it's quitting time. That's simply a fringe benefit of doing a real production. (It's not like Kate and Leo were gonna walk out the back door of the Multiplex when Titanic was over). The charm of theater is that they go home when you go home, so a chance encounter is an extra treat.
Problem is there has to be compromise and when over-eager fans meet I-wanna-go-home performers, it's not always going to go smoothly. It's hard to be a chipper actor/actress when you've been doing it for so long and now you know there is an extra 10-15 minutes, possibly, waiting between you and that meal or you and your after show television before bedtime.
Sometimes it's better to just see the show, hang and give them a smile. Don't go near them, just be silently supportive. Keeps you from getting slapped. :)
Just my worthless two cents. In 20 years of doing this, I've seen it all...and it wasn't always pretty.
"Sticks and stones, sister. Here, have a Valium!"