This year's volatile mix of religion and politics has stirred at least as much controversy in churches and synagogues as on the campaign trail.

Well before the last balloon popped at the Republican National Convention in Dallas last month, religious leaders on both the right and the left were speaking out on the extraordinary role religion played in the political arena there.

While most tend to agree that religious beliefs should influence an individual's political behavior, there is far less consensus on how -- or whether -- politicians should deal with religious questions.

Among the issues that have drawn the most comment are President Reagan's charge at a prayer breakfast that those who oppose school prayer are "intolerant of religion;" Sen. Paul Laxalt's "Dear Christian Leader" letter to Texas clergymen urging voter registration drives in churches to "help secure the reelection" of the Reagan-Bush ticket; and Democratic vice presidential candidate Geraldine Ferraro's charge that Reagan is not a good Christian because he cut programs to aid the poor.

With few exceptions, Jewish leaders took offense at the Laxalt letter and the president's judgment on those who oppose school prayer.

So did Claire Randall, general secretary of the National Council of Churches. "To brand as intolerant of religion those with sincerely held, theologically based religious opposition to school prayer or any other matter that differs from his chosen position," Randall said, "falls far short of the standard of tolerance for the beliefs of others which must undergird religious freedom in a diverse society."

On the other hand, Robert P. Dugan Jr., director of the Washington office of the National Association of Evangelicals, found the president's address at the Dallas prayer breakfast an indication that "he has thought through the relationship of religion to politics."

The president's assertion that "politics depends on morality and morality depends on religion," said Dugan, is "helpful for the national debate."

But Robert Maddox, a Southern Baptist preacher who heads Americans United, complained that Reagan is "dividing the nation rather than healing it."

Maddox, once an aide to President Carter, wrote President Reagan urging him to "rethink your efforts to promote a religious agenda for the campaign and as a matter of public policy. . . . Please, Mr. President, back off from the religious rhetoric before you fuel fires of distrust and prejudice."

The American Jewish Committee also warned of the danger of unleashing dark forces of intolerance, in a comprehensive statement on "Religion and American Pluralism," that was drafted before the Republican Convention began. "Erosion of the principle of church-state separation in the United States has reached serious and disturbing dimensions," said the statement, which was drafted Aug. 8.

"The highest levels of individual and institutional leadership . . . have taken actions that could weaken pluralism in American life," the committee statement warned.

To remedy these and other threats to religious pluralism in this country, the American Jewish Committee has launched a "national Religious Freedom Education Project," forming coalitions with other religious groups with similar concern.

Their first effort will be a press conference in New York today, where Jewish, Protestant and Roman Catholic representatives will join in an appeal to both the Democratic and Republican parties to "oppose all efforts to tamper with the First Amendment."

Seeking to draw a line between appropriate and inappropriate involvement of religion with politics, Eugene J. Fisher, who heads the office of Catholic-Jewish relations for the National Conference of Catholic Bishops, told a Jewish gathering earlier this week, "It is perfectly valid for people of a religious persuasion to put forth their ideas. But it must be done in ways that can be debated in the public forum."

As members of a religious minority, leaders of Jewish groups have been particularly concerned that church-state separation is maintained. They were consequently nervous over the Christian imagery and rhetoric that abounded during the Republican convention.

Rabbi Alexander M. Shapiro, who heads the National Assembly of Conservative Rabbis, accused President Reagan of "Christianizing America . . . All religious groups must be very careful about arrogating to themselves a total knowledge as to what is God's will and what is absolute morality," he said.

Despite arguments for keeping religion and politics in the proper relationship to each other, there is widespread agreement that precise distinctions are hard to draw.

As Hyman Bookbinder, who heads the Washington office of the American Jewish Committee and helped draw up that agency's statement on the question, acknowledged, "We need to acknowledge that we don't really know how to draw the line between the acceptable and the unacceptable."