"How clean of power does someone need to run a modern TV and some speakers and maybe the margarita blender?"
That could turn on the definition of "clean".
In terms of inverters, I have had no trouble with MSW for doing those kind of things. PSW is required for a few special things like electric blankets and other things as listed in the guides for the MSW inverters where they warn about that.
Microwaves are more complicated, where some don't run on MSW but some do, just slower. Some work and run slower making horrible noises, same noises as they do on PSW that has too low a voltage where the 120v supply is on too long an extension or overloaded in a busy park.
The MWs I have had in the last 15 years do ok on MSW, just taking longer to "cook", but even taking longer they draw fewer amps because of the way they get their input from AC, so they have the inverter pull fewer AH from the battery bank to get it done. (more H but less A in the AH where A counts for more )
Some info on inverters and dirty power and MWs and TV picture and radio interference from the 1990s does not seem to apply so much these days it seems. EG the OEM 1990 Dometic RV MW in our C does not run at all on MSW, but does fine with PSW. The MW we had in the 2003 5er had no issues with MSW except to run a bit slower. So they did something back then to the newer MWs.