DishWASHER detergent is a no-no...but dishwashing liquid is ok
So what if it sudses a little...a few bubbles out the vent won't hurt anything.
I'm guessing that you want to clean out the tank ahead of winterizing. So first, pump out the tank and THOROUGHLY rinse it out to get rid of any sludge before you "clean" the tank walls.
If you're gonna use enough Dawn or something similar to do any good, you'll prob'ly need a whole bottle of it in a tank full of water...go sailing and tack a lot...then let it stand at least overnight. Pump out (or dump offshore) and thoroughly rinse again...then winterize.
This should be as often as you need to do it.