In the sauna there are untreated wooden benches and they get stains if they get wet. Wet bathing suits are REAL a problem for them. That is why you should ALWAYS be seated on your CLEAN towel with all parts of your body that come into contact with the wooden benches.
Bathing suites all have some sort of techincal fiber - be it lycra or what ever. Have a closer look at your bathing suit - it normally cannot be washed over 30 dergrees C never mind 60 or higher. Towels however can be washed at 90 to 95 Degrees C and are therefore far more hygienic.
That is why you should have a LARGE clean and dry towel for inside the sauna to sit or lie on (optionally a small one the wipe your sweat off) and then a regular towel to shower with.