We full-timed for 16 years and used the town laundries and have NEVER found them to be dirty. These 'horror' stories are passed down and embellished in my opinion. Pick a laundry in a decent part of town and you will not have a problem.
The washers wash and rinse the clothes. Commercial washers have multiple rinse cycles.
At your house do you put your dirty underwear, vomiting clothes or work clothes in your washer? Do you sanitize your washer afterward?
The clean clothes are put into the dryer. How can the dryer be dirty if they dry clean clothes?
We are very particular and clean people. We have absolutely no qualms about public laundries.
We always found that town laundries have personnel working in them.