Williams, 25, attended Santa Fe Christian in Solana Beach, Calif., which rejected the San Diego Union-Tribune's efforts to visit the school for a story about the actress' roots.
"We don't want to have anything to do with her in relation to that movie," headmaster Jim Hopson told the newspaper.
"Michelle doesn't represent the values of this institution. We would not approve of her movies and TV shows (including the teen drama "Dawson's Creek"). We'd not like to be tied to 'Brokeback Mountain,'" he said.
"I hope we offered her something in life. But she made the kinds of choices of which we wouldn't approve," he continued. "'Brokeback Mountain' basically promotes a lifestyle we don't promote. It's not the word of God."
Williams will be at the Academy Awards Sunday night with her fiance, father of her child and "Brokeback" leading man Heath Ledger. Ang Lee's film is up for eight Oscars, including Williams' best supporting actress nod.