Of course, you should always leave your black tank valve closed until the tank is full or at least 3/4 full. You should not skimp on water in the black tank because this water helps keep everything in your tank solvent. I think everyone agrees.
The grey tank being open or closed seems to cause much controversy. Here's my take.
During normal use the grey tank does collect some unwanted residue from dishwashing such as crumbs, food, soap scum and grease. Grease could potentially be the worst thing sitting in your tank. It can become insoluble and cake on the sides and bottom of the tank.
It makes sense, if you leave the valve open, some grease will naturally drain with any liquids. It also makes sense some grease will solidify on the bottom of the tank and some will solidify around the valve. On the other hand, if you leave your valve closed, much of the grease will stay on top of the water some may solidify on top of the water once the water cools. Very little will accumulate around the valve area, but some will always cling to the sides.
If you keep the valve closed, which is what I do, when you open it, the force of the water should wash most of the debris and grease out. If you leave it open, it would make sense to close it a day or two before emptying your black tank to flush your sewer hose. Once in awhile, you could partially fill your grey tank with warm water to liquefy any grease build up around the valve area.
All that being said, one must remember, when leaving your valve open, you are leaving it open to the campground sewer. I have heard of instances of worms or bugs swimming past the pea traps and coming up through the kitchen sink. This is probably very rare, however, it seems very possible they could be swimming around in your tank. Why this doesn't happen at a bricks and sticks, I don't know. Of course we've all heard of the stories about rats and snakes coming through the sewer lines.
Whether you choose to leave it open or closed, most RV'ers don't have a problem, open or closed. The argument for leaving it open seems to be one does not have to remember to open it every couple of days and face grey water coming through the shower drain. It could be a problem if you have a lot of people taking showers.
I say it's a personal choice.