Think it out. Sitting on towels is like wearing pants.
In a textile environment you go from seat to seat and your "towel" is attached at the waist. In a restaurant, office, or other public space you don't think twice about sitting on the next available seat, regardless of who sat there previously. Because you have that layer of fabric between you and the sitting surface.
In a nude world, the surface contact is more personal. So using a towel is equivalent to wearing pants. The only thing you have to consider is which side of the towel to use. The easy thing to do is to use printed towels ( or use a fabric marker to put a mark on one side ). Then use only the right reading or marked side to sit on. Been doing that for ever.