Here in the divorce capital of America, home of the National Gay Rodeo and the "World Ladies Oil Wrestling Championship," where Miss Nude America prances the stage in flamingo-pink plumes while casinos hum and call girls hustle through the night, President Reagan is winning votes because of his fundamentalist stance on social and family issues.

It's not that most people here approve of Reagan's embrace of the Rev. Jerry L. Falwell or his demand for an abortion ban and organized prayer in public schools. In this live-and-let-live gambling town, a large majority seems to believe that religion and morality are not government's business.

But among the minority of Renoites for whom "moral decay" is the paramount issue of the day, Reagan scored heavily with his speeches on morality and religion at the start of this campaign.

"It's a very smart issue for the president because it only helps him," said Peter Sferrazza, Reno's mayor and the state Democratic chairman. "People who agree with him -- that's what they vote on. The majority may disagree, but they're voting on the economy or defense or whatever."

"I suppose there are people who object to the president's use of religion, but I think they're the ones who are already voting for Mondale," said Jeanine Triggs, coordinator of a local fundamentalist coalition. "But there's a huge population of Christian people who have been shut out of politics, disenfranchised really, because they thought it was dirty or something. And all of a sudden, here's Ronald Reagan, and he turns these people on."

Triggs said she came face to face last summer with the political power her minority might hold when her group, the "Reno Pro-Family Christian Coalition," was circulating petitions to ban the annual gay rodeo from the fairgrounds.

"We would get people to sign against this homosexual rodeo, and then we'd say, 'Are you registered to vote for Mr. Reagan?' " she recalled. "We got literally hundreds of people who had never wanted to vote before."

Because it is difficult to gauge people's core feelings on the social issues in the campaign -- delicate matters such as abortion, religion's place in government, homosexual rights and women's status in society -- it is not entirely clear to what extent Reno reflects the nation.

But most politicians and pollsters said that the Reno pattern would hold in most places, that Reagan would get more votes from those concerned about moral issues than he would lose among those who fear invasion of privacy if government tries to define and enforce morality.

The social issues have been more visible this time, partly because Reagan made them so, particularly in a speech the day of his nomination about the link between government and politics, and partly because Mondale fought back.

The Reagan administration gave the conservative "social agenda" low priority in its first three years.

But in 1984, Reagan stepped up his appeals for a constitutional amendment banning abortion. His administration also took a strong, new antiabortion position at the United Nations conference on population in Mexico City last summer.

When the Senate last spring defeated an amendment authorizing voluntary prayer in public schools, Reagan fought a compromise permitting only silent prayer. He demanded sanction of vocal, teacher-led prayers in the classroom. The vocal-prayer proposal was rejected 56 to 44, 11 votes short of the required two-thirds majority.

At the Republican Convention in Dallas, Reagan invited Falwell, leader of the fundamentalist Moral Majority, to give a benediction. The minister declared that Reagan and Vice President Bush were "God's instruments in rebuilding America."

On the last day of the convention, Reagan broached the religion issue at a huge prayer breakfast. He said opponents of his school prayer proposal were "attacking religion."

"Isn't the real truth that they are intolerant of religion, that they refuse to tolerate its importance in our lives?" he said.

"The truth is, politics and morality are inseparable," Reagan said. "And as morality's foundation is religion, religion and politics are necessarily related . . . . Our government needs the church."

This statement drew at least as much attention as Reagan's convention acceptance speech later the same day.

Mondale decided to address the issue.

"No president should attempt to transform policy debates into theological disputes," Mondale told a B'nai B'rith convention. "He must not let it be thought that political dissent from him is un-Christian . . . . Instead of construing dissent from him in good faith, Mr. Reagan has insulted the motives of those who disagreed with him, including me."

Here in Reno, and perhaps nationally, the emergence of social issues probably has been a plus for Reagan.

Reagan's association with Protestant Christians may have cost him some support among Jewish voters, according to Rabbi Abraham L. Feinberg, who warned in a column in the Reno Gazette, "If Moral Majority . . . Christians are able to have their way in the selection of the president, they might have a stranglehold on the political coloration and destiny of this country."

But Reagan's antiabortion position may win some support from Roman Catholics. The head of the local diocese, Bishop Norman F. McFarland, has urged parishioners to support antiabortion candidates.

And there is no doubt that Reagan's clear association with the Christian right has sparked hundreds who had not voted before to register so they can support him.

"The media all condemn us for being single-issue voters," Triggs said. "But when you remember that about half the people in the country have no issue that makes them want to vote -- isn't one issue better than none?"

In general, however, people in this city of 120,000 seem to want the preachers and the politicians to leave each other alone. And they indicate that they will vote for their own reasons.

Adjusting her black mesh nylons and micro-skirted uniform, a casino waitress named Sonia -- "No last names for customers" -- took a break from serving the gamblers.

"Now this abortion, that's not what I think is up to government, you know?" she said, rolling back on her four-inch stiletto heel. "Leave that private stuff up to people, you know?"

And will this effect Sonia's vote?

"Okay, you're right, if that was the only thing, I suppose I should vote against Reagan, is that it?" she said. "But I think we're doing okay in this country now. I'm sticking with the president."