I don't think it's fair to assume that it's the vast majority. Some, definitely. You just need to avoid pushing it. I went to one the other week where I was told to undress and lie down. No towel. That's clear enough sign that HR is available. If they drape a towel over you and don't go anywhere near your groin or buttocks then it's safest to assume that HR isn't on offer.
Just treat all the masseuses how you'd want, say, your own daughter to be treated. With respect.