This is what Sammy was talking about, filters
. That will give you the general idea of how to use filters, and the filter entity you would want to use for this would be filter_activator_team.
The unfortunate thing is that there's not actually a filter field on the door entities though. Even turning off SmartEdit and adding the filtername field manually, it doesn't appear to work. Though it's possible I'm just missing something and somebody else may know of another way to do this.
Assuming it's not possible to get the filter field working on doors, the alternative solution I would take is to make a brush that is roughly the size of the door, one unit wider on each side, and apply a NoDraw texture. Tie this brush to a func_button and you will have a key value on the func_button for Only Allow Team. Just set this to the team you want to allow to press the button. Then put an output on the button to open up the door.
Hope that helps, and hopefully if I'm wrong about the filter on the actual door entity somebody will come along and correct me.