> Of course, discriminating in this way is already illegal for normal rentals, but when you have rentals of rooms in people's houses I believe it actually is legal for hosts to discriminate in some cases.

In California (the rules on this vary considerably by jurisdiction within the US), there is generally very little limit on discrimination by those renting out a room to a single roomer/boarder (but not if they are renting to multiple roomers/boarders), in an owner-occupied single family dwelling, though they generally can't advertise preference on any protected axis except gender, and only for that when there are shared living areas.

In a case like this, renting out the entire place when the terms of the rental is that the owner won't be there, this exception wouldn't seem to apply, though Idaho may have different rules (I'm having more trouble quickly finding a good description of Idaho's rules.)