In fact prohibited on Sundays: most tenants do it anyway
The holiday laws of the various federal states govern what is allowed on Sundays, which is why they also differ depending on where you live. However, publicly visible activities that disturb the tranquility of the day are generally prohibited.
This also includes, for example, Laundry hanging in the garden or on the balcony. Although it does not make noise, people might feel disturbed if the area is visible to third parties.
In practice, very few people are likely to be really bothered if you hang your laundry on a Sunday. After all, many employees can only do these household chores and other similar tasks on weekends.
Other than that, you need to make sure that your washing machine doesn’t wash harder than the volume of the room on Sundays. If the device is uneven and rotates at high speed, it may disturb the neighbors. If your washing machine is in a common room, the law may also prohibit Sundays.