I suppose. But the primary part of what the parents are paying for is a religious environment. You obviously think their religion is nonsense (which is your right). But the parents wouldn't want their children around someone who rejects the tenants of their religion --- otherwise they'd go to public school.
FWIW, I attended a yeshiva in Israel where there was a homosexual teacher who was an Hasdic Orthodox Jewish man. He was permitted to teach, provided : (1) he signed an agreement (and abided by it) that he would remain completley celebate while teaching and (2) that he agreed and accepted the religious instruction that homosexual sodomy is a sin and wrongful behavior and would not argue otherwise.
As far as I knew, he abided by it.
Perhaps that could work as a compromise. My understanding of Christianity is limited, but I understand they do not object to a person having homosexual urgings, they merely object to the performance of the same. ("Love the sinner; hate the sin.")
I understand that might be a difficult feat for you, but maybe not.