I would say the average door that has a good fit to the frame will hold the 300 or so pounds. Once the straps are tight against the door and frame, all that weight is being pulled straight down on the door. Those hinges should take most of the weight pretty easy. Make sure all the screws are tight!
Having said that, it is a "Sex Swing" right? So the next problem is whether the door is hollow or solid. Some of them hollow doors are pretty thin and it would not take much to break them.
One more consideration is the latch/lock. You don't want the door coming open in the middle of things, eh?