Dribblers anonymous gathering. No shirts, all the liquid.
Before I brush my teeth, I have to remove my shirt, or I end up with toothpaste stains all over it, so I'm definitely going to be a founding member.
The exposure is only indecent if you're a laundromat or dry-cleaner owner. Thick walled mugs are a conspiracy by big laundry to make us wash more garments.
Therefore, by removing your shirt before "dribbling", you're saving the Earth by wasting less fluid on washing.