You're not special for washing dishes in a less efficient way that's worse for the environment. If you've just never had access to one, ignore me, but Ive definitely known a surprising number of people who have dishwashers in their apartments but refuse to use them. If that's you, you're probably doing life wrong.

Anyway there's nothing that unique about the dishwasher itself, washing cast iron in hot soap and water and then leaving it to air dry will strip the protection of the polymerized oil and then trigger the pan to rust. Nothing to do with dishwashers as a technology except if you wash a pan by hand you're likely scrubbing it less effectively and not willing to spend 1-2 hours spraying it with hot water. If you stick the pan into the washer for 15 mins, immediately rinse, dry, and re season, it's not particularly different from washing by hand.