What is the ruling on entering a room belonging to a family member during the day, if the door is not closed and it is customary to allow entry without seeking permission?

If entering the room is customary and done without seeking permission, and the owner's consent to this is known, then there is no harm in entering it. This is because customary permission takes the place of verbal permission, and knowing the rightful owner's consent takes the place of their explicit manifestation of consent.