I've long noticed that many hotels seem to have a SOP that maids and room service workers prop the door open; I've never noticed a place where housekeepers seemed to be required to close the door while they are in the room, even if they're allowed to turn on the radio or TV. I would assume that any housekeeper who isn't a thief would prefer that the door be open.

I also know a few hotels have women's floors, where room service is delivered by a female and I've also seen this pattern in certain large higher end properties, such as in Tokyo. I imagine that many properties would allow female guests to request female room service delivery if they have female staff available.

Another example is a USA higher end hotel (SPG LC) that has male housekeepers who are always sent in two-person teams, perhaps because both don't speak English, but this could also protect the hotel legally.