Use 3 prong microwave on 2 wire ungrounded outlet?
You can use a three prong adapter, but only if you can ensure that the adapter is properly grounded.

An AFCI/GFCI outlet will help with some scenarios, but those outlets are meant to be grounded.  If you install one without grounding it, you're going to confuse whoever comes along later (and sees a 3-prong outlet) into thinking that the outlet is grounded.  So don't do that.

Another problem is that the microwave's chassis, if not grounded, might act in certain circumstances like an antenna and radiate microwaves into the room.  That would cause a lot of interference with other electronics (especially WiFi gear), and could be harmful.

Lastly, there could be some capacitative coupling that would cause an electric charge to build up on the chassis, leading to a shock hazard.