Washington — Politically, President Reagan won. Although the school prayer amendment went down to defeat in the Senate, 56 to 44, Mr. Reagan has scored points with his religious constituency on the right. He pulled out all stops on behalf of the amendment - jawboning in public, importuning senators at the White House, making last-minute phone calls.
He gets credit for the effort. That, say Reagan strategists, is what counts in the election campaign.
''No one expected it to pass,'' says a key campaign operative. ''We could see the votes were just not there. But Reagan was on the side of an 80 percent popular issue, so he will get credit with the Christian community.''
Not the whole Christian community, however. Almost all major Protestant groups - and Jewish groups as well as civil-liberatarian organizations - opposed the prayer amendment, voicing concern that the President is playing politics with religion and contributing to sectarian divisiveness in the nation.
''We think Reagan has a fundamental misunderstanding of the proper role of church and state,'' comments Joe Conn, spokesman for Americans United for Separation of Church and State. ''Traditionally the majority of our political leaders have been personally religious and supportive of religion, but they have not politicized it the way Reagan is doing.''
Whatever the deepening national controversy over church-state and social issues, the President will continue to court Roman Catholics and fundamentalist and evangelical Protestants who cast many votes for him in 1980. He now is expected to press for tuition tax credits for parents sending their children to parochial and other independent schools as well as for antiabortion legislation. Recently, too, he established full diplomatic relations with the Holy See, another move with electoral pulling power.
''This has been an important debate, revealing the extent to which the freedom of religious speech has been abridged in our nation's public schools,'' the President said after the school prayer vote. ''The issue of free religious speech is not dead as a result of this vote. We have suffered a setback, but we have not been defeated. Our struggle will go on.''
Reagan went on to urge Congress to consider ''equal access'' legislation. This law - several bills are pending in both chambers - would permit voluntary student religious groups to meet on public-school premises as do other groups. In general, this legislation is less controversial. Some versions are supported by the National Council of Churches and legislators who opposed the prayer amendment.
Even while he maintains his ties to his constituency on the right, however, President Reagan is moving toward the political center as the election campaign gathers momentum. There will be less public wooing of the right coalition, according to campaign strategists. This follows the pattern of previous elections, when Reagan first consolidated his right flank and then moved into the political mainstream on the dominant campaign issues.
President Reagan has not been much in the front-page news recently. But Reagan campaign planners now are looking for events and occasions - business forums, union gatherings, and the like - where the President can focus on the economy and try to grab political support and media headlines.
''Scheduling will have to be more attuned to mainstream events that capitalize on the good news,'' a campaign operative says. ''The economic news has been extraordinary.''
White House planning is also under way for the foreign travels which will give Reagan an opportunity to play the pragmatic statesman and look presidential. Next month the President journeys to the People's Republic of China for a six-day visit that will entail heavy media coverage. On the way, he will make a stop in Alaska to meet with Pope John Paul II - an event also calculated to please Roman Catholic voters. In June he goes to Europe, where he will visit the Normandy beaches, make a sentimental trip to Ireland, and attend the economic summit in London.
Meanwhile, Reagan campaign advisers are careful not to pronounce publicly on the Mondale-Hart contest that has dominated the political news. ''We're letting the Democrats run their race,'' says one highly placed official. ''We'll run against whoever wins.''
Yet there is quiet satisfaction among GOP strategists that Walter Mondale did well in Illinois, putting him firmly in the race, and that Gary Hart has lost some of his momentum. As one put it, ''It's a 50-50 contest now, and the tougher and longer they fight the better for us.''
Among the perceived strengths of the senator from Colorado is his popularity with young people and his demonstrated ability to capture the vote of independents. The latter is a voting group Reagan needs to co-opt again to win in November.
Running against Mr. Hart in November would also deprive the Republicans of the strategy of linking the Democratic nominee to the failed Carter administration. Hart could be assailed for his liberal record in the Senate, it is felt, but because he is not in the traditional mold of a liberal Democrat, he could move toward the center of the political spectrum more quickly. This, too, could pose a challenge for the President.
On the other hand, on the plus side for Mr. Mondale, GOP strategists believe he could go into a election having better united the disparate elements of the Democratic Party. It is also believed that, because of his experience, he would make few mistakes and that he would have greater appeal to older voters.
But Reagan operatives insist there are no current plans for changing campaign strategy. ''Our campaign is adept at running an effective campaign, whoever is the Democratic standard-bearer,'' says an official at the Reagan-Bush campaign committee. ''We will wait until the process works itself out.''