I'm never hooked up "permanently" but when we have full hook-up sites and we are staying for a few days, I go ahead and hook up my sewer hoses together. I have no problems dumping my tanks.
In the photo below, the front drain is the kitchen sink. The back drain is the shower (grey) and toilet (black) that join at a common outlet. I do not leave tanks open and when draining, drain them one at a time.
On the back one, I have a 3rd valve (Flush King style), so I can close off the common outlet and use that to back flush the grey water into the black tank to help rinse it out without having to pump a lot more water down the black tank. This simple process saves a lot of water and cleans the black tank out very well. If you are parked long term in one spot, this is a very good method to use to flush out the black tank.