water pressure

Are you sure your cold water supply is not being shared elsewhere such as a fresh water tank fill valve in the wrong position etc etc

Look at the pump. Water still goes through it. Might be two lines one to hot water and one for cold water side.
Pump might have more pressure and force it to the faucet. Unscrew the aerator and see if it comes out. Might have to take the valve out at that water point.
There is an obstruction, in the cold water side, pipes, since you took off the filter. If you can squeeze the pex pipes you might giggle it down stream whatever it is and then maybe not.
Any RV Plumbers here?
Just for the heck ,of it check the fill valve selector. It would seem both sides would be affected if it was only partially in position.

Which filter you use makes a big difference in water flow at faucets. Should be no noticeable pressure difference between hot and cold water. May have a restriction in cold water line. Remember pressure is not volume.

Probably needs a new filter. The filter itself will cause a little pressure loss.
Maybe input water pressure is low too.