I think sweat patches bother people.
That's curious. Why would people be offended by sweat patches?
Okay, then I'll tell you how I feel. Yes, they do bother me.
You shouldn't judge others just because they sweat. Think about how you would feel if someone judged you for your physical appearance.
It's hard to stop breaking out into a sweat in the heat of the moment but they should do something about it.
But like you said it happens in the heat of the moment so they cannot prepare for it. You need to stop judging people for sweating, it is a normal body function.