I often run my pump when connected to city water in places (usually on a well) where the water pressures drop so low that I don't have enough pressure to suit me when I am showering. It doesn't hurt the pump at all. As city water pressure drops the pump comes on and will pump from the fresh water tank until the pressure comes back up above the pumps set point.
Noise is often due to the water pipes/tubes vibrating against the structure. Sometimes it can be fixed by mounting the pump on a thick pad and using flexible lines to and from the pump.
Winnebago did all of that but somewhere between the pump and the bathroom faucets the line vibrates and causes more noise than I like. I have just learned to live with it.