Just FYI, you do wash cast iron, you just don’t use detergents on it. One common method is to dump a handful of salt and a tiny splash of water into the pan and start scrubbing. You can use a gentle dish soap, but I’d avoid using the dishwasher, because those detergents will be a lot stronger and will actually ruin the seasoning (as well as linger on the surface and end up in your food, which is also bad).
Modern soaps/detergents don’t contain lye, which is what ruins the seasoning. It’s the humid drying of a dishwasher that causes it to rust. Nothing to with the detergent.