If you speak to an actor openly, or if you are friends with a working actor, most will tell you that the stage door is very draining. I am not going to argue with people on here who say "its not hard to smile,sign, take a photo, be filmed for 30 seconds, etc" because you really are being quite close-minded.
Many actors are introverts by nature and doing the stage door every night for years on end (for many working actors) can become difficult. Also, most of us have some level of vanity and like "good" photos of ourselves and dont like to be snapped at with cameras and filmed from all angles when tired or trying to go home.
See most of you are looking at it solely from your own perspective and you see it as its not a big deal for ME to ask them to sign, take a photo, but you fail to see is YOU are not the only one asking. It happens every night on a loop, before the show, after the show, on the street.
Then in addition to the regular lot of sweet, kind, respectful, appreciative theatre-goers (like most of you on here I imagine fall into that category) there is a handful of needy, stalkerish and poor-boundaried souls who can make an actor uncomfortable, especially when you are dealing with shows with cult followings (RENT, SA, N2N).
So, in closing, try to think about the bigger picture and realize how nice it is when actor will sign or take photos and kindly respect and not bad mouth when they do not.
"The sexual energy between the mother and son really concerns me!"-random woman behind me at Next to Normal
"I want to meet him after and bang him!"-random woman who exposed her breasts at Rock of Ages, referring to James Carpinello