No harm at all. In fact it is an advantage.
The pump has a outlet check valve to make sure the water runs through the pump when pumping and cannot backflow either when pumping or when the house pressure is higher.
In fact, low pressure at the post is a common problem at campgrounds especially when everybody decides to shower at 7AM in the morning. Keeping the pump on means that if there is insufficient pressure from the post the pump will kick in and make up the pressure and flow. You have to keep water in the fresh tank to do so or the pump will just spin with no water flow.
What happened with the shower, the flow is typically higher than other use. At 40 PSI post supply on the inlet the pump pressure switch (on the outlet of the pump) saw a low pressure than set point and kicked on the pump, giving more flow and pressure to the shower. Most of these pumps are set for 50-60 PSI and can be field adjusted. With your supply at 40PSI the pump was trying to get you to 60 PSI, hence the pump did it job.
I would change your regulator to 50 PSI as the house plumbing can take up to 75-100 PSI will no problems. But you may need the pump on at some campgrounds to keep the DW content in her shower.