Washington — Could President Reagan's conspicuous injection of religion in the political campaign backfire? Political observers are asking whether the Republicans may be damaged to some extent politically because of the President's strong comments in Dallas about the inseparability of religion and politics and by his unabashed courting of religious groups.
''Reagan is trying to portray the Democrats as antireligious, and it's not true,'' says William Schneider of the American Enterprise Institute (AEI) in Washington. ''This could create problems for him, because, while Americans are deeply religious, they also believe deeply in the separation of church and state. So there could be a backlash.''
As concern grows about the President's position and news media highlight the issue, the Reagan-Bush campaign is being forced to respond. Asked on the CBS ''Morning News'' Monday whether using evangelical Christians to woo support for the Republican ticket violates church-state separation, Vice-President George Bush replied: ''I find it a little peculiar that when we have people who agree with our values and agree with our administration's policy, suddenly we're talking about mixing church and state. We are not.''
Mr. Bush said GOP support for groups like the evangelical Christians, who are busy registering voters, is no different from Jesse Jackson's urging of black voters to register. ''All last year, Jesse Jackson had his message go out through the pulpit, and I thought that was fine.''
Several Democratic governors, meantime, in a meeting with Walter Mondale this past weekend, suggested that the presidential candidate challenge Reagan's views on the issue of religion and government. Virginia Gov. Charles S. Robb, for instance, was quoted as saying that the Moral Majority leader, the Rev. Jerry Falwell, was ''the most unpopular person in the state.'' The implication was that Mr. Mondale need not fear making religion an issue in the campaign.
Advocates of church-state separation are concerned, however, that playing up the religious issue into the heat of a political campaign would simply polarize the country further and be counterproductive. ''Mondale has good credentials as a church man and it's better for him to stay out of it,'' says Robert L. Maddox, executive director of Americans United for Separation of Church and State. ''This is not the way to have a debate.''
At the same time AU officials suggest that while Reagan has picked up fundamentalist votes, he is losing support among conservatives. Mr. Maddox says that about half the membership of Americans United - which comprises about 40, 000 individuals and 4,000 churches and synagogues - are Republicans and that, especially since the establishment of US diplomatic ties with the Vatican, the organization has been receiving ''a steady drumbeat'' of letters from members saying they are going to vote against Reagan because of the church-state issue.
Catering to the religious right, Reagan has sharply attacked critics who oppose his policies on such issues as a constitutional amendment banning abortion, school prayer, and tuition tax credits for parents who send their children to private schools. Speaking at an ecumenical prayer breakfast in Dallas last Thursday, the President suggested that ''those who claim to be fighting for tolerance on this issue may not be tolerant at all.''
''I believe that faith and religion play a critical role in the political life of our nation and always have ... The truth is, politics and morality are inseparable - and, as morality's foundation is religion, religion and politics are necessarily related. We need religion as a guide. We need it because we are imperfect, and our government needs the church because only those humble enough to admit they're sinners can bring to democracy the tolerance it requires in order to survive.''
The AEI's Mr. Schneider says the President is reaching out to fundamentalist believers, who tend to be on relatively low income levels and who vote Democratic. Because many of these voters cannot be appealed to on economic grounds, he says, Reagan is using the themes of religion and nationalism - themes heavily accented during the GOP convention.
The President's speech has drawn strong criticism. Writing in the New York Times on Monday, conservative columnist William Safire said the President and his campaign chairman, Sen. Paul Laxalt, have ''turned truth on its head by suggesting that those who are trying to preserve the separation of church and state are guilty of intolerance....''
Says James Dunn of the Joint Baptist Committee: ''Reagan's comments are one more evidence of the total lack of sensitivity to church-state separation and the American tradition of religious liberty that appeals for civility, respect, and distance when it comes to the use of religion by political parties.''