Is rubbing alcohol allowed? A resident is using it for aftershave.

What type of resident? Are we talking assisted living or memory care? Your profile says he's in AL but has dementia. Does the person know he's using rubbing alcohol? Does he think it's after shave? Have you told him it's alcohol? Does he seem confused at times? Have you noticed any changes in his judgment? You offer little information. Nevertheless, the rubbing alcohol must go. Don't replace it with actual after shave. People with dementia do not discern what is dangerous and what is not. He may mistake it for something drinkable. That would be horrific! If he insists on an aftershave, you can either offer an aftershave balm or, better yet, water with food coloring to look like aftershave. Discard the alcohol.

Wouldn’t alcohol dry out his skin?

It is a bit harsh on the skin.
Can an aftershave be provided to him?
If he wants to use the alcohol I would dilute it at least 50/50 with water.
PLEASE make sure he is not drinking it.