I've been to campground where the tenters wash themselves and their dishes in the community sink that dumps directly onto the ground. I've also seen people brushing their teeth at the water spigot and spitting toothpaste onto the ground. I don't think a little shower effluent is going to do more harm that that. Of course, most campgrounds prohibit these activities and an open hose spewing water would probably attract attention.
However, water is your best friend when it comes to keeping the black tank from plugging up. If you're having capacity problems, I'd consider a waste tote instead.
Tote