As I see it there are several issues:
The religious issue is just that and although I don't agree with Northrup's interpretation of what is morally right, he certainly has his right to an opinion and I commend him for sticking up with it.
The idea that any touching of the opposite sex in a non-sexual activity is forbidden simply because it involves the opposite sex is more bothersome to me. I believe that women are more than just a sexual object and that we need to interact with them at all levels in society. Teaching kids that girls/women can be dealt with for who they are and not by the 50/50 chance of their gender doesn't seem to me to be a bad thing. Inherent with this lesson is that inappropriate behavior can be inappropriate regardless of the venue. Teaching what is appropriate behavior should be a part of every adult's interaction with kids.
Along the same vein, what if a wrestler were gay? I would find it hard to believe that there is not a gay wrestler in the state of Indiana. It would be that wrestler's responsibility to treat his opponent with respect and not behave in an inappropriate manner. Say that wrestler "came out". Would they have the right to wrestle for the state championship? How would he feel if he won the state championship just because no one would wrestle him?
Finally, the whole bit about chivalry. If a girl wants to wrestle (and to do so at this point requires her to wrestle boys), the last thing she would want is to be treated with deference. If you truly respect her, then try to pin her if you can. That is what she would want.