FYI - What you just experienced is cultural sexism. It's extremely common in many cultures around the world.
It used to drive my coworkers nuts when we were traveling internationally. They would enter a meeting and everyone would still be speaking their native language. I would enter a few minutes later and everyone would switch.
The only place they didn't switch languages at all was France. They don't give a fuck equally.
Good dishwashers have a heating element on the bottom. . It turns on and dries the dishes in a cloud of steam. There is also a button on mine that's for high heat (sanitize) that I leave on. This ensures that the dishes get completely dry.