I suppose it's a matter of the solvents in all LSPs. Even non-cleaner/straight waxes will effect a little cleaning; ever hit some residual dirt with your wax applicator and then notice that it's soiled?
TOL used to sell a cleaner-wax called Snap Seal that was made just for this; as best I can tell it's basically a high-solvent liquid wax. It cleans off tar and left some LSP protection. Haven't used it in ages, but I still have a jug or two on the shelf.
Back in the '70s some of us used Meguiar's #7 as a mild cleaner, it worked OK.
I usually clay such stuff off myself, or use a solvent if redoing the LSP is worth a quicker removal of the tar.
Be careful using textured media with solvents, all such stuff that I've tried marred paint for me, it looked especially awful under magnification. I won't even use "bug sponges" on painted surfaces, though I do like them for glass. I use very soft cloths, letting the solvent do the work rather than relying on mechanical action; if I want to employ a mechanical method I'll use clay.