In Singapore (of all places) many apartments have one of their toilets right next to the kitchen. Seems to be fine.
But they have a door, right?
Yes, of course, we are not barbarians.
(Just to be clear: I think doors on bathrooms are great. I just don't think they really contribute to hygiene or health--apart from mental health.)
Airborne fecal contamination from flushing is likely reduced by having a barrier