"Rubbing Alcohol" such as that sold under the commercial name "Isocol" is typically Isopropyl alcohol. I can confirm that Isopropyl alcohol (I have tried 99%) is not at all compatible with Tamiya LSP.
On the other hand, denatured alcohol aka methylated spirits (as mentioned is ethyl alcohol with added components to render it undrinkable), can be used to thin/clean Tamiya LSP.
This is reversed for Mr Surfacer, which can be cleaned up using Isopropyl, but not denatured alcohol.
Both Mr Surfacer and Tamiya LSP may be thinned using either (GSI Creos) Mr Color Thinner or Tamiya Lacquer thinner (both of which are relatively styrene friendly), or a generic hardware store lacquer thinner, which may be harmful to styrene.