Our painter got lots of primer on our old hardwood floors, thinking we would cover them with carpet. Should this be sanded off or stripped before sanding?
Well, that was a pretty big presumption on the part of your painter! In your situation, I would scrape as much of the primer off as you can, by hand, before following up with sanding. Depending on how that goes, you might have to do more heavy sanding than usual - which is unfortunate, because every time you sand hardwood, you take life out of it.
I recommend the U-Sand Pro Sander over a four-belt sander, which is harder to control and takes off a lot of wood. The U-Sand features four rotating discs and drops sawdust into a bag.
You shouldn't have to physically strip your floor. Stripping would mess up the finish underneath, and could only make the job a lot worse.