My kitten Newton is fascinated by the washer/dryer (then again, my kitten is fascinated by just about anything that moves). She 'paws' at the washing machine porthole/window when the clothes are spinning around. I have a stacked dryer, and fortunately, he can't jump high enough to get into the dryer himself. I've placed in inside the dryer compartment briefly to snap a few cute pics, but that's the only time he's gotten anywhere close to it.
Having said all that, one of my kitten's new resting spot is the clothes hamper - he jumps in there whenever he wants some peace and quiet.
When I'm not at home, I keep both doors to my bathroom and washer/dryer closed. Since I have two cats, it's not uncommon for one cat to stroll in, and the other one to push the door closed behind them (inadvertently, I imagine, not that I can be 100% sure). Both those areas are only accessible when they're supervised