We have been fulltime now for 5 years, with two different 5th wheels. We have always left the gray tanks open, present 5th wheel has two gray tanks, other had one. I do keep the black tank closed and dump every few days. I have opened the black tank a few times, if you do, make sure you use A LOT OF WATER. Your home commmode uses about 1 gallon of water, per flush. I did not leave the black tank open with old 5th wheel. The new one has a raise system in the black tank, and when we do leave it open, I used it once a week, and use LOTS of water. Also, we use a bath tissue that breaks down easy, (it's kind of crude but it works, take a piece of tissue of the kind you want to use, throw into the toliet, then have "the man of the house" use the toliet, if the piece of tissue breaks up, it is good, if not get something else). Scott Extra Soft, is what we have used, it breaks up very easy, and many others use it, also with no problems.
It is up to you of course, but I have no problems leaving the gray tanks open.
Hope this helps God bless,