OAKLAND, Calif. — The Roman Catholic Diocese of Oakland is under fire for a new contract clause that requires teachers to conform to church teachings in their private lives.

Some parents, teachers and students worry teachers could be fired for being gay or engaging in behavior the church frowns on, such as having sex outside marriage.

Five teachers have refused to sign the new contract, Diocese of Oakland spokesman Mike Brown said this week. Parents and teachers also plan to protest at the diocese’s offices Friday.

The diocese runs more than 50 schools and employs about 1,000 teachers, many of them non-Catholics. Brown told the San Francisco Chronicle this month that the new language is not a witch hunt, but an attempt by Oakland Bishop Michael Barber to be clearer about the contract.

“It simply states what was inferred before from a new bishop’s perspective,” Brown said. “There is no list of behaviors from this diocese.”

But some teachers see it differently.

Kathleen Purcell, a history teacher at Bishop O’Dowd High School in Oakland, said she signed the contract, but crossed out the part about private behavior. The section reads: “In both the employee’s personal and professional life, the employee is expected to model and promote behavior in conformity with the teaching of the Roman Catholic faith in matters of faith and morals, and to do nothing that tends to bring discredit to the school or to the Diocese of Oakland.”

Her contract was not accepted, and she does not plan on returning to the school.

“I could have taken back what I did and said I could go along, but I can’t do that,” Purcell, 62, told the Oakland Tribune. “My life is about advancing civil rights.”

The issue has come up in Ohio as well, in a new contract proposal from the Archdiocese of Cincinnati. The Catholic diocese in Cleveland has introduced a similar contract.