You asked it two different ways, in the title you asked if they'd need to keep the door open (my answer is 'no'), but in the body text, you asked if I would allow them to close the door (my answer is 'yes').
But, I grew up in the 70s, so people weren't so uptight then, at least the parents I dealt with weren't. So, I didn't have any rules for my son, and, had I had a daughter, I wouldn't have had any rules for her.
In fact, I'd be happier if they were at home, they'd be safe at home.