This usually means Serratia marcescens, an airborne bacterium that settles on damp surfaces. It usually is not coming from the water.

It lives on soap and shampoo residue in a warm humid room, which is why it shows up in the shower and the toilet rim and nowhere else in the house.

Look for pink only where surfaces stay wet, worse in a bathroom with a weak fan, and nothing pink in a glass of water drawn from the same tap.

Do not buy a filter for this. A filter treats the water, and the pink is arriving through the air. Cleaning and ventilation are what move it.