The MX missile program, a massive mobile nuclear system that nobody seems to want in his backyard, found itself with a new and perhaps lethal opponent yesterday -- the Mormon Church.

Declaring that the missile system was "a denial of the very essence" of the church's gospel of "peace to the peoples of the earth," the First Presidency of the Church of Jesus Christ of Latter-day Saints asked the nation's leaders not only to keep the MX out of Utah and Nevada but to find an alternative plan altogether.

The Air Force wants to deploy the mobile missile system in 4,600 bunkers spread throughout the Great Basin desert home of the Salt Lake City-based church. The plan has run into widespread public opposition in the area, with the governors of Utah and Nevada declaring they don't want it. t

But the church's opposition was unusual, strong and carried exceptional political weight. In a 2 1/2-page statement, church president Spencer W. Kimball and his two counselorsm, N. Eldon Tanner and Marion G. Romney, essentially made the missile system a moral issue.

The Mormon Church rarely takes formal political positions, although it also has opposed the Equal Rights Amendment on moral grounds. When the church president offers such opinions, Mormons believe his statements are inspired by God.

Kimball said he found it ironic that the Mormons, who retreated from religious persecution into the Western deserts in the 19th century to "establish a base from which to carry the gospel of peace," now find themselves sought after as the host for a weapon "potentially capable of destroying much of civilization."

Kimball's statement said the world is engaged in a "terrifying arms race" that has to be stopped. "We deplore in particular the building of vast arsenals of nuclear weaponry. History indicates that men have seldom created armaments that eventually were not put to use.

"We are most gravely concerned over the proposed concentration [of the missiles] in a relatively rstricted area of the West," the church said. "Our feelings would be the same about concentration in any part of the nation."

In their statement, the Mormon elders said the concentration of missiles would mean "one segment of the population would bear a highly disproportionate share of the burden, in lives lost and property destroyed, in case of an attack, particularly if such were to be a saturation attack."

The Reagan administration is expected to recommend a method of deployment for the controversial weapons system in early July. The system is expected to cost from $35 billion to $60 billion, with 200 multiwarhead nuclear missiles shuttled through the 4,600 bunkers in an attempt to confuse potential Soviet attackers.

The Air Force says the system is needed because land-based Minuteman missiles, also deployed throughout the West, are becoming more vulnerable to increasingly accurate Soviet missiles.

"With the most serious concern over the pressing moral question of possible nuclear conflict," the church elders said, "we plead with our national leaders to marshal the genius of the nation to find viable alternatives which will secure . . . protection from possible enemy aggression which is our common concern."

The church has 4.7 million members, including 1 million in Utah comprising 70 percent of the state's population. Both of Utah's Republican senators, Jake Garn and Orrin G. Hatch, are Mormons and strong supporters of increased defense spending.

The strong home-state opposition to the missile system, however, has left Garn and Hatch walking a political tightrope. Yesterday, a Garn aide said the senator would study the church position closely and make a statement today. Hatch also was biding his time.

Hatch said the church position "reflects many of the major concerns we Utahans have." But he said he would await the results of a final government study of the missile's impact "before any final decision is adopted."

In Chicago, Defense Department Secretary Caspar W. Weinberger, informed of the Mormon stance, said, "This is very interesting. Of course, we will consider viable alternatives. . . .

"I think we are all agreed that we do need the missile. The question is where do we put it?"