I'd rather use a product *made* to strip the wax, but rubbing alohcol (straight or mixed with water) works well too. In my experience, dish soap (e.g., Dawn) doesn't really strip wax very well. Doesn't dent products like #16 or Collinite, even when used in strong mixes. Vinegar won't hurt anything and might work on the water spots, but IMO it's not the best way to remove wax.
Only problem with just polishing through the wax is that you might get a messy residue. Not a huge problem, but sometimes (e.g., using PI-III MG to cut through KSG) the residue can be very hard to buff off. A quick spray with a rubbing alcohol/water mix and a wipe with a MF will at least remove *most* of whatever LSP is on there, and it only takes a moment.
I don't get the "claying will remove wax" thing...I've clayed for well over a decade (since detailing clay came out), do it almost every time I wash, and it sure doesn't strip my LSP :nixweiss Having experimented with claying through LSPs, I just can't imagine that people clay this way on a regular basis. Whenever I tried intentionally claying through my LSP, I had to be so aggressive about it that I was claying incorrectly and risking marring.