NEW YORK — Thomas S. Monson, who as president of the Church of Jesus Christ of Latter-day Saints since 2008 enlarged the ranks of female missionaries but rebuffed demands to ordain women as priests and refused to alter church opposition to same-sex marriage, died on Tuesday at his home in Salt Lake City. He was 90.

Facing vociferous demands to admit openly gay members to the church and to recognize same-sex marriage, and weathering demonstrations at church headquarters by Mormon women pleading for the right to be ordained as priests, Mr. Monson did not bend. Teachings holding homosexuality to be immoral, bans on sexual intercourse outside male-female marriages, and an all-male priesthood would remain.

Mr. Monson displayed a new openness to scholars of Mormonism, however, allowing them remarkable access to church records. But as rising numbers of church members and critics joined the Internet’s free-for-all culture of debate and exposé, his church was confronted with troubling inconsistencies in Mormon history and Scripture. The church even found itself at odds with an old ally, the Boy Scouts of America, which admitted gay members and gay adults as scout leaders.

On Mr. Monson’s watch, the church enlarged its global missionary force to 69,200 from 52,000 and, in what students of church affairs called a major achievement of his tenure, doubled the number of young women in its missionary ranks, to 18,400, by lowering the minimum age for service, starting in 2012, to 18 from 19 for men and to 19 from 21 for women.

“That sent shock waves through the church,’’ Richard Lyman Bushman, a Mormon scholar and Columbia University historian, told The New York Times. At 21, he said, many Mormon women were married and not free for missionary work, while lowering the age to 19 let them become missionaries soon after high school.

“It changed the whole view of what women would do, that they would go just like the men,’’ Bushman said. “There was a great surge of readiness. It changed their mentality.’’

Despite persistent demands for change on another feminist issue, Mr. Monson — who as president was considered by adherents to be God’s “prophet, seer and revelator’’ — did not open the door to women in the priesthood.

As the 16th president of the Latter-day Saints, succeeding Gordon B. Hinckley, Mr. Monson opened the church archives, allowing historians access to church documents and records to a remarkable degree. In allowing such access, students of church policy said, Mr. Monson presided over an unprecedented era of openness about church history, while reassuring the faithful that theirs was the one true, unerring faith.