The top hinge of our shower door is pulling away from the wall, which causes the door to sag and leave a little gap when it's open. I tried pushing the hinge back into place and tightening the screws, but they simply can't be tightened anymore, and I don't want to strip them. What is the easiest way to fix this?
Whatever the screws go into is no longer holding.
So you need to find out what it is and then redo the support there.
If it is wood then I would drill a larger hole and glue a wood dowel in there and, once dry, drill pilot holes and resecure with the screws or even new screws.
If brick / masonry, t6hen perhaps gluing rawlplugs in may work or drilling and fitting larger diameter plugs may work.