If it's their own room and they're alone, they've been allowed to do that since they were..3 or so? Well, my boys can be in there together and still close the door, as they share a room. Keep in mind that the rooms have always been fully childproofed, including furniture straps and passive outlet covers, ect.
With friends, the door must always be open slightly.
The kids are 8, 7, and 7. Though I have to say, whenever we have friends over the kids spend little time in the rooms or even in the house--they're always out exploring our property and building forts in the lilac bush or running through the ferns.
We are open with our kids about the appropriateness of body exploration with other kids (not appropriate), which typically is the main concern that I've heard people raise with giving children privacy. We've also been open about how self-exploration is fine, as long as it is private.
When I was worried about the kids choking on toys or sticking forks into the sockets, I kept direct line supervision of them and playdate friends. Now that I don't have to worry about that (as much), and they know the rules for guests and the consequences of breaking them, I see nothing wrong with allowing semi-privacy. I think bringing up concerns directly, rather than denying privacy because you want to make sure to catch them, tends to work a lot better.
That being said, our kids also understand that they do not have full privacy, nor the expectation of it. They don't have independent locks on the doors (though we always knock). We can and do occasionally look through the contents of the DSes and will do so for computer accounts in the future as well. Even at this age, I do generally check in on playdates (even if they're running through our property) about every 45 minutes or so.
So with all that stuff, closed doors is probably not the greatest privacy concern--our wooded and bushed property is. But with a combination of supervision and communication, so far we've not had to deal with any uncomfortable situations.