You can wash Cast Iron all you like, I wouldn't suggest the dishwasher, just don't use soap, scrape with a plastic paint scrapper under hot water, heat until smoking, rub some oil on it, let cool. Easy peasy. After knowing we're all poisoning ourselves with the nonstick coating and have been for decades, the Cast Iron is a great nonstick alternative.
This thread is full of people claiming that dish soap doesn't contain lye, but the most popular dish soap I'm aware of, Dawn, contains lye and that's easily found in a two second Google search.