It is a myth that you can’t use dish detergent on cast iron. If it feels greasy and filthy, it is greasy and filfthy.

The truth behind the “no soap” myth is that we used to use lye-based soap for dishwashing. Lye does, indeed, break down seasoning. But we use surfactant-based detergents now, rather than actual soap. Detergents break down oils, but they don’t

Your boomer parents/grandparents couldn’t wash their cast iron with dish “soap”. You can.