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Not if you're constantly using it, but yea if you leave it it will get mouldy.
Here's the faff explained by Hario:
It is really important to clean the cloth filter straight after it's been used. Rinse it under running water until the majority of the ground coffee is gone. Boil some water and soak the cloth twice for about 10 minutes each time. This should remove all the coffee oils and coffee fines from the cloth. Once the cloth filter is visibly clean, let it dry. If you use it frequently/daily, it’s better to leave it damp in the refrigerator inside a zip-lock bag.
Wouldn’t they get mouldy then?