Because any editorial that appears under the Deseret Media masthead carries the unofficial imprimatur of the church in many Mormons’ eyes, Deseret editors and executives could indeed help shape opinions in the heavily Mormon state Legislature, where lawmakers are debating a zero-tolerance illegal immigration law similar to the one passed in Arizona this year.

For the time being, church leaders seem uninterested in wading into the debate by taking an official policy position, as they did by declaring support for the referendum to ban same-sex marriage in California. Rather, it has made only a benign public appeal for “careful reflection and civil discourse” on the issue. But that has hardly soothed matters.

That the main sponsor of the Arizona law, Russell Pearce, is a Mormon has not been lost on many Hispanics here. And some active Mormons said they thought that the church, through its media properties, was trying to reassure Hispanics who were suspicious that it condoned anti-immigrant attitudes.

“Some of my Latino friends have said, ‘I’m going to leave the church over this,’ ” said Tony Yapias, director of Proyecto Latino de Utah, a Latino outreach group. “My view is that this is an aggressive way for the L.D.S. church to very effectively use their media power to try to soften up the community. They’re sending a message to their members.”

Both Mr. Cannon and Deseret Media’s chief executive, Mark H. Willes, said they never sought approval from church officials on any editorial or article they ran. They said the church also never asked to see an article before it was printed, though former editors said the practice had been to fax drafts of editorials to church headquarters.