I want to say the 1994/1995 “Priest” was this one.:
“Father Greg Pilkington (Linus Roache) is torn between his call as a conservative Catholic priest and his secret life as a homosexual with a gay lover, frowned upon by the Church. Upon hearing the confession of a young girl of her incestuous father, Greg enters an intensely emotional spiritual struggle deciding between choosing morals over religion and one life over another.”
“A priest tries to reconcile his love for another man with his love for God, but when a girl steps into the confessional and reveals that her father sexually abuses her, he’s frustrated by the laws of the church and questions his faith in a God who would allow this to happen.”
So, I don’t know if the original article author got the year of “Priest” mixed up with the 2011 vampire version (“A priest disobeys church law to track down the vampires who kidnapped his niece.”) or if he got the 2011 plot mixed up with the 1994 priest-with-a-gay-lover-who-questions-why-bad-things-happen-to-good-people. I remember hearing something about stripping him of his producer credits, so I’m not seeing him credited on either movie at IMDB… but I don’t know if that’s because he’s higher up the food chain, or because he’s been erased.
The NYT review from 1995 seems to indicate that Weinstein’s was the gay-priest movie, though.