Washington — To a greater extent than in the recent past, religious and church-state issues are emerging as a major element of a presidential campaign. Both Republicans and Democrats have injected religion into this year's political contest. President Reagan is doing so by his active courting of religious constituencies - fundamentalist Christians and Roman Catholics - through support for such policies as prayer in the schools.
The Democrats, determined not to let Mr. Reagan seize the high ground of religiosity, are mounting their own campaign for ''traditional values.'' They are also signaling that Roman Catholic officeholders will not seek to pass laws that embrace their own personal beliefs on controversial questions like abortion.
Any presidential election year finds candidates suddenly more sensitive to religion. Often they resort to moralizing or start going to church more often. But political experts see the religious factor more dominant this year than in recent elections, although the emphasis is different.
''It's more salient this year than in '64, '68, '72, and '80,'' says American historian James MacGregor Burns. ''This is due to Reagan's ideology, to the fact that he considers himself religiously oriented. It's not a matter of political guile but the fact that religious fundamentalism and the issues which he emphasizes - abortion and prayer - have a natural linkage with political fundamentalism on the right.''
Other observers also see today's mixing of religion and politics not as a manifestation of religious divisiveness but of ideological differences over public policy.
''In 1960 (when John Kennedy ran for president) the question was specifically a religious one,'' comments political scientist Richard Scammon. ''It was whether the Roman Catholic Church was building a tunnel from the Vatican to the White House.''
''Today the question is one of ideology with religious overtones,'' he says. ''Both abortion and tuition-tax credits for parochial schools are ideological and political questions. If they were purely religious they would not have the alliance of Catholics and fundamenalist Protestants and some Orthodox Jews.''
President Reagan, more than any recent President, has pushed public policies that raise church-state issues. Aside from school prayer, he is vigorously backing tuition-tax credits for parochial and other private schools. He would like a constitutional amendment outlawing abortion. He has supported legislation to strip the courts of authority to rule on abortion and other issues. He has also established US diplomatic relations with the Vatican, and exploited every opportunity to spotlight his cordial relations with the Pope.
There has been little negative public reaction to most of these policies. Mr. Reagan has broad popular support for prayer in the schools. But civil libertarians and many religious groups, particularly mainline Protestant clergymen, are concerned about what they see as a gradual erosion of the separation of church and state.
''We have never had in history a president who evidenced less understanding of the First Amendment as a safeguard of religious liberty and a bastion to protection of the separation of church and state,'' says James Dunn, executive director of the Joint Baptist Committee. ''So this is an empirical difference in the way religion and politics are being related.''
Americans United for Separation of Church and State takes a similar view. ''Religion is going to be a bigger part of the election than at any time since 1960,'' says spokesman Joseph Conn. ''In 1980 the Moral Majority was very active but now more denominations are involved, with the candidates clearly vying for votes. But breaking society into blocs and then appealing to these blocs is not a wholesome development.''
The President's conspicuous appeal to religious sentiment has sparked a response from the Democrats. Rep. Geraldine Ferraro, the vice-presidential candidate, had to backpedal on her slur on Reagan's Christianity. But the Democrats are trying not to let the GOP co-opt religion-related policies or moral issues.
In his keynote address at the Democratic convention, Gov. Mario Cuomo of New York suggested he would not judge the President's divorce from his first wife or impugn his Christianity because he has not seen his own grandchild. And recently he criticized the archbishop of New York for questioning how a Catholic could vote for a candidate who explicitly supports abortion.
Mr. Cuomo, who is opposed to abortion, says nonetheless that he does not favor a government ban on abortion and that people should be able to make their own choice. This, in turn, drew a statement from the Bishop James W. Malone, president of the National Conference of Catholic Bishops, arguing that political figures cannot a draw a line between ''personal morality and public policy.''
Walking through a political thicket on the issue, Walter Mondale has stuck by his freedom-of-choice position. He also opposes tuition tax credits for parochial schools, a position on which Ms. Ferraro has reversed herself in order to be in step with the Mondale position.
''I'm uncomfortable with all the vying over religious and moral values in the campaign,'' says Mary Cooper, a spokesman of the National Council of Churches. ''We would prefer to see the debate shape up over the practical application of moral values.''