SALT LAKE CITY — Ever since she was an infant being blessed during a church naming ceremony, Lindsay Matson had been on the books of the Mormon Church. As it has done with millions of other members, the church kept note of her spiritual life as she moved from congregation to congregation, took youth leadership posts and married at age 19 in a Mormon temple.

But now, she and other Mormons upset over new church policies that declare same-sex couples apostates and restrict their children from baptism and other rites are venting their objections by demanding that their names be struck from the church’s meticulously kept records.

During the weekend, Ms. Matson and two daughters, one of whom is gay, joined more than 1,000 people lining up in a park here beside the church’s temple spires for a mass resignation. Most had not been to church in years, but they described deep ties: They had grown up in the Church of Jesus Christ of Latter-day Saints, gone on missions, raised their children as Mormons. Even as their faith and attendance ebbed, they remained members on paper.

“There’s a constant contact when your name is on the record,” Ms. Matson said. “The church considers itself responsible for you.”