Prevent a painted door frame & door from getting paint on each other?

I would leave the door open to wait for the paint to dry.

there should be a small gap between the jamb and the door so they don't touch each other when painted. if the door is chafing the jamb, you will need to sand it where they meet or cut with saw. if you are talking about cabinets, leave door open until dry and install rubber bumpers on all corners after they at dry

Try using a piece of wax or a candle.Coat the opposite non painted side with wax. Just rub it where the door meets the frame. I can’t say what the exact thickness of the wax should end up being. I just rubbed it over the areas a few times. This will also work on painted drawers so they don’t stick.