I am Chozar Teshuva so if this is a ridiculous question then please bear with me.
Long story short, my cat soiled a ballcap that I own (soil as in, with urine). I put it through the dishwasher, got it nice and clean. Is it considered ritually impure? Like would I be able to wear it at all? Would things I put on my head or touched after touching the hat also be impure?