Coke, when you take a job you should make it clear what you are willing to do and what you just can’t do. So if you are uncomfortable folding personal items that is what you should say. “I don’t mind folding general laundry or young children’s clothing, but I am not comfortable folding personal items such as parents’ or young adults’ underwear. Be upfront about it.
If there is someone in charge of sending girls out to do cheesed, then you can ask them to let the clients know about a young person’s sensitivities to this issue.