I think it is harmful to say that masks protect the wearer (unless they are N95 or better). This is a big and easily attacked surface that only serves to obscure and discredit the real point of wearing masks.
Instead the messaging should focus solely on the fact that they protect others from the infection carried (likely without knowledge) by the wearer, and that people without symptoms can be contagious.
This point needs to be drilled into people's heads until everyone gets it. People also need to be taught to wear masks properly. Wearing one with nose sticking out is darn near useless.