I was always told to let them fill before dumping. Otherwise you create a bunch of sludge in the tanks and lines. Dump valves that don't close properly could also happen from build up. The rush of water keeps everything flushed out. Have never had tank problems doing it this way.
I always leave all of my tanks closed until they are full and then dump them. I also put treatment in them to keep them clean, both gray and black. I have not had any problems with tanks but always keep them closed. I have also heard they gum up and it does make sense because the water goes out and the sludge stays behnd.
Joe, that's exactly what we are doing because we found that with showers and the washing machine we could fill that grey tank up in less than a day but our galley tank fills about the same rate as our black.