The issue of religion-and-government has emerged in this year's presidential campaign in a way that neither President Reagan nor Walter F. Mondale had intended, and its prominence has unsettled strategists for each campaign, if for different reasons.

Mondale yesterday capped two weeks of sporadic attacks and anticipation with a full-scale assault, accusing the Reagan administration of welcoming the efforts of a "determined band . . . reaching for government power to impose their own beliefs on others."

Both camps report that Mondale's criticism of Reagan and the Republicans on this issue may be weakening support for Reagan among a group of young, moderate swing voters.

But Mondale advisers say they are eager to move to less emotional issues. "We would rather not be in a political squabble over these questions," a senior Mondale campaign adviser said. "This is not the place to try to turn a political election ."

So the Mondale aides said they hoped the Democratic nominee's speeches yesterday to the B'nai B'rith and the predominantly black National Baptist Convention would douse the fire of this controversy rather than fan its flames.

Reagan political strategists are eager that he not retreat from his support for school prayer, right to life and other pet concerns of the religious fundamentalists -- and they are certain he will not.

"Any vote that Reagan is going to lose because he supports school prayer or abortion he lost long ago," said one Reagan official.

But the Republican strategists say they would prefer he affirm his religious views in non-sectarian tones less likely to arouse the liberal social dander of working-class Catholics and young independents drawn to Reagan's economic policies. So when Reagan spoke to the B'nai B'rith yesterday only hours after Mondale gave his well-publicized speech, he focused on U.S. policy in the Middle East. He passed up a chance to lock horns with Mondale in absentia, as the two had done on arms control and defense issues in back-to-back speeches Tuesday and Wednesday to the American Legion national convention in Salt Lake City.

The roots of the current debate over religion and government stem from the 1980 campaign, when the Rev. Jerry L. Falwell's Moral Majority and other fundamentalist groups championed the cause of conservative candidates.

Mondale's running mate, Geraldine A. Ferraro, fired the first major shot of the general election campaign season on July 13 in Elmore, Minn., ridiculing Reagan's claim that he was a "good Christian" on grounds that his budget cuts were "terribly unfair" and discriminatory.

Later, New York Gov. Mario M. Cuomo differed with New York Archbishop John J. O'Connor over the role that the abortion issue should play in politics.

Then came the Republican National Convention in Dallas late last month, with strident statements from religious fundamentalists and Reagan's assertion at a prayer breakfast that "religion and politics are necessarily related."

At that point, Mondale advisers decided that the Republicans and Reagan had gone too far. Ironically, the Republicans had reached the same conclusion, sensing that enough had been said about religion to mollify concerns of the fundamentalists.

Democratic strategists said Mondale, the son of a Methodist preacher, felt his religious credentials were under challenge. But they acknowledge that Mondale's defense of religious freedom fit into the Democrats' plan to portray the Republicans as outside the American mainstream.

"We're not the kind of people, in other words, who . . . say you either believe the way I do or I'll hang a label on you," a senior Mondale adviser said.

Mondale had his say on the issue yesterday, and stirred enthusiastic responses from both his audiences.

Mondale may now be content to move on, but his aides will be watching the responses of two important audiences.

One is the Democratic strategists outside the campaign who repeatedly have faulted Mondale for calling off his attacks when Reagan appears to be retreating.

The other is the public. Strategists for both candidates will monitor public opinion to see if there is any more to be gained -- or lost -- by keeping the emotion-laden issue alive.