Sinead O’Connor sings the gospel at Alice Tully Hall

To the casual observer, it could sound like hypocrisy, if not downright blasphemy: Sinead O’Connor — the woman who will be forever known by some as that crazy bald chick who ripped a picture of the Pope on TV — will perform two concerts this weekend devoted entirely to reverent odes to God.

Tonight and tomorrow at Lincoln Center’s Alice Tully Hall, O’Connor will be flanked by titans of gospel music, including the Soul Stirrers and the Inspirational Voices of the Abyssinian Baptist Church.

“I’m a bit of a religious maniac,” O’Connor says. “At the same time, I’m a bit of an antireligious maniac.”

Let her explain: “Religion and God are two different things. God needs to be rescued from religion.”

Serious fans know O’Connor has been working to untangle faith from formal churches and temples for years — both in her role as a public figure and in her music. Between 2002 and 2007, the Irish star released three full CDs devoted to spirituals of one sort or another. And for decades O’Connor has been listening to songs by genre icons like Mahalia Jackson, Sister Rosetta Thorpe and the Soul Stirrers.

The roots of this weekend’s show go back to last year, when O’Connor appeared at the Lincoln Center Festival tribute to Curtis Mayfield. “I performed his great song ‘Jesus’ and buggered it up quite badly,” the star admits. “Despite that, they asked me to do a whole gospel show.”

O’Connor considers Mayfield’s piece “the best song ever written about Jesus. The line between corny and cool is extremely fine. And Curtis managed to stay on the right side of it.”

As a kid, O’Connor didn’t hear many God-oriented tunes that she considered cool. “The Ireland I grew up in had awful religious music,” O’Connor says. “It was ‘Drop Kick Me Jesus Through the Goalposts of Life,’ ‘Kumbaya’ or ‘This Little Light of Mine.’”

It wasn’t until Bob Dylan’s first religious album, 1979’s “Slow Train Coming,” that she started to rethink the genre. “Dylan made it cool and sexy,” she says.

O’Connor found herself drawn to religious music that “wasn’t about being perfect. In fact, it was about being very imperfect.”

The singer’s most recent CD “How About I Be Me (And You Be You)?” makes pointed critique at organized religion in “Take Off Your Shoes.” The song, O’Connor says, “wonders, ‘What if the Holy Spirit were a character — what would he have to say to the Pope?’ He would have a chat about all the cover-ups and abuses.”

The singer says she has “no issue” with the new Pope. She takes some satisfaction, though, in the fact that her original protest against the then-pontiff back in 1992 — music fired by sexual abuses in the church — has since been globally acknowledged. “We knew 10 years before you did what was going on,” she says.