We have left both open in the past....but then there was the time sewer gasses came back at us.
then in Mississippi, I saw several large slugs coming up the pipe. I just laid our pipe outside and recapped it. When we emptied and flushed the black and then the gray next morning, after connecting, we gave them a good bath.
When we are using the washer we leave it connected. one shower each and one load, of clothes, and maybe some dishes, the tank is full. our Gray tank is 100 gallons same as potable water. We have had a bit of water in the shower.
Instructions say to and we do have it connected and open when we wash clothes and some other times. Many times we check gauges before showering, if parked a while and open, then. Closed night before to fill with as much soapy water, as possible to flus the system.