Freshwater tank taking in water from unknown source...

Depending on how your rig is plumbed up, what others have shared regarding a leaky valve or check valve, that would be the cause.

A leaking check valve can be the result of a dirty valve ball and/or ball seat. You could try bleaching & flushing your system to clean it.

On rare occasion something physical may have gotten lodged in the check valve. People have had trouble with tiny plastic debris left from when holes were drilled in the fresh water tank during the construction of the rig. It can take many years to get into bad places.

Sometimes that debris can be sent on it's way by running the on-board pump. Just be sure to take off the running faucet's aerator to let the debris out.

Maybe you could open the fresh water tank drain, and leave it open, so that you could tell when the tank is receiving water. That might enable you to tell something about the problem.

enblethen wrote:
Water back feeding through the pump is a possibility.

X2, I close the suction valve to the pump to stop the flow of water into my tank when on city water. I changed the check valve in the pump and it worked for a short while then quit working again. Closing the valve works just fine for me. JMO

Do you have two separate fill points, one to hook the hose to for city water & one you stick the hose into to fill the tank? If so, I'd go along with enblethen & say the pump.

A check valve installed in the line. It can go either before or after the pump. Best is after as if you have a complete pump failure, you could still have city water.
Depending on make and model of pump, you could take pump apart and find the small amount of debris causing the back feed.

I had the fill valve on the right to leak when hook to city water causing the fresh water tank to fill and over flow. Yours could be leaking.

Put a backflow inline after the pump.

If it's back feeding through the pump, you might need to replace the pump itself to solve the problem.

However, if you really never use it, just replace the T junction where city water and the pump outlet join up with the house plumbing with a straight connection between city water and the house. This bypasses the pump and tank entirely. Problem solved. Probably for < $5 in parts.

I do not. Hasn't been a problem. Could that be why?

Speaking of water preesure, do you have a water pressure regulator on your hose or RV connection ?