"Making allowances" means to "allow things" ( by extension: to accommodate, cut slack for, etc).
If you have a friend who has trouble walking, and the two of you fly together to Florida, you "make allowances for your friend" by carrying their baggage, or pushing their wheelchair through the airport, and like that.
You said that your friend "acts badly". So you know they were talking about his behavior. If he moves out, and has room mates, or gets a job, the folks around him who aren't his family may not put up with his horsecrap the way his family does. Ergo "they wont make the same allowances for him" that the family does.