Fear not solids in the tank. Yes, there is risk, but it is not that substantial if the rules above are followed - especially keep some water in the tank.
Personally I will use the park restrooms but that is more as a courtesy to my family. It is a very close environment.
I would prefer my kids use the camper toilet though since I like to know that the surfaces they are touching have only our germs on them. I have my own habits that protect me but they are a bit too young to be paranoid enough to maintain the same germaphobia I have developed through years of media exposure.