Baseball team refuses to play with girl

So, recently there was a kerfuffle in the news regarding two baseball teams from rival Catholic schools. One team had a girl as the second basemen, and though she chose to sit out two games against the rival team, out of respect for their beliefs (of not playing against a girl I guess?),she refused to sit out the championship game. Not surprisingly, the rival team forfeited, because,  "Our school aims to instill in our boys a profound respect for women and girls. Teaching our boys to treat ladies with deference, we choose not to place them in an athletic competition where proper boundaries can only be respected with difficulty."

Here is the article: http://www.newser.com/story/145814/catholic-school-boycotts-title-game-over-girl-player.html

So all this got me thinking. How would you handle this sort of thing as a parent, booj? Would you have encouraged her to sit out the games, or to play them? Sit out the championship game? If your kid wanted to play in a sport that was predominately played by boys (baseball, football, etc.), would you let them, or would you be afraid of them getting hurt/teased/what have you? How would you explain to a younger child this idea of gender segregation?

Discuss!

ETA: or conversely, how would you handle this situation if you were the parent of one of the boys on the rival team, and they didn't want to play against the girl? Assuming you had chosen to send your kid to a "fundamentalist" Catholic school.