My name's not Johnnie.
Seriously I think its a deregoratory term for any backstage staff, but particularly the stage door keeper, who vets who comes in at this particular door.
You miss the point, Firefly. A stage-door Johnnie is a 'Hooray Henry' type who hangs around the stage door trying to pick up one of the ladies from the show, possibly because he thinks showgirls are 'easy'.