If you can’t change the water source, change the way you rinse. Do a final rinse with cold water. I know, I know—brrr. But cold water helps close your pores and stops mineral residue from settling back in.
Or, here’s a wild idea: keep a spray bottle of filtered water in the shower. After you wash your face with hard water, spritz your face with the filtered stuff. It’s a quick cheap hack that feels slightly ridiculous, but it works.