What is the religious objection?
One objection he stated was that he didn't want to be "physically aggressive" with a girl. I'm assuming his religion is Christian. I can't think of any Christian rule that specifically says you can't be aggressive in sports with girls, but he also said he had personal reasons not to do it.
As a Christian, I would see two problems with co-ed wrestling. First would be the close, physical contact between people (especially teenagers) of the opposite sex, that aren't married to each other. As a Christian, I would be teaching any teen boy I might someday have to keep his hands off girls, even if it's the spirit of friendly competition. Wait 'til you're married. The whole, if you like, put a ring on it thing. Second would be the current move toward de-emphasizing or denying differences between the sexes. The Bible isn't misogynistic, but it does treat the sexes as having different qualities, and different roles. Some Christians think it's our responsibility to remind the current culture that those differences are real. So there could be a Biblical reason to say no to integrated athletics.