even then the table will stit stably on the slope. The tabletop will not be level with regards to the horizon/gravity but that is not what the theorem requires. It only requires stability (i.e. no "wobbling")

Yes this might not be entirely practical if you try it on one of the famous sloped roads in San Francisco but for most other parts of the world (restaurants, cobblestone sidewalks, etc.) it will be good enough from a practical standpoint :)