My sister makes herself out as a victim because I put her laundry in the dryer

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If she's stopping you from doing your laundry, maybe ask her, "Hey, can you move your clothes to the dryer so I can do mine?" If she doesn't do it, then either put them in the dryer or move them to a clean hamper.

If no one else is needs the washer/dryer, why should you care? Let her clothes get musty from sitting all day.

I've lived in a house with 6 other adults and laundry is just going to be an issue sometimes. You can make a laundry schedule, or ask in a group chat if anyone else needs to do laundry before you (and others) start, or just agree to touch each others' clothes.
He/Them
"Am I a butterfly dreaming I'm a man... Or a bowling ball dreaming I'm a plate of sashimi? Never assume that what you see and feel is real!"