I think it's time he put his own clothes away, on his own hangers, in his own closet.

I wouldn't say a word about it and don't react emotionally. It's good you just hung the clothes on "his" hangers and didn't respond with throwing his on the floor.
Without saying anything, buy him his own laundry basket for his laundry. If you can find a matching black one- great but if not, be sure it's a different color than the ones you use- this is going to be *his* laundry basket.
That's where his clothes go if you take them out of the dryer. If he wants them hung up - he can do it himself. No need to say anyting- just leave them there.
This is a form of "natural consequences". He can have his own hangers if he wants, and so can you. No big deal. But if he's going to throw your clothes on the floor, that is disrespectful behavior. You were thinking "his and hers" - sharing. He wants his own- so OK- his hangers, his closet- his clothes- are his responsibility. You continue to keep your cool. It's just another way to manage the laundry.