Gay rights for Christian school employee

My cousin is coaching for a Christian school. She is living with a family (her girlfriend's family), going to college nearby and coaching part time for this school.

The athletic director approached her yesterday. He warned her that the HR woman said she has seen that my cousin is in a gay relationship and living with her girlfriend and does not think it is appropriate for her to work with the girls at the school. The athletic director has said it is not an issue and has not been a problem. He made it clear to her that he does not judge others.

In other words, her private life has remained private and she would never discuss any part of it with the girls. She is coaching them in sports, not her private life and respects all the values of the school during her interaction with the teams.

It seems there is someone in the office who is also a mom of a girl on the team that the athletic director suspects is "stalking" her social media. I gave her the advice to make sure all her social media is private as she plans on working with children after college and should always whatever her situation is to keep her private and media accounts separate from her work life with children.

I am familiar with public schools as I work there and know this would not fly at all, but what about private and with Christian in the name? The school is not associated with any church but is noted as Christian and that you agree to follow Christian values. At this point she just wants to keep the job until end of next month when the season ends and has no desire now to continue after the season.

I know from reading on here that you cannot give legal advice, but just want any advice or thoughts or experiences of others.