President Reagan has put his arms around the New Right agenda - a move that worries moderates but thrills many of his staunch, conservative supporters. The Reagan move has been particularly pleasing to advocates of school prayer and federal aid for parochial and private schools. It has also been gratifying to foes of abortion. Fundamentalist preacher Jerry Falwell looked at the GOP platform adopted here and proclaimed: ''It's just like I wanted it.''
The strong Republican move toward such religiously based New Right positions raises several important issues to a new level of discussion for American voters. It also creates serious political problems for the Democratic Party.
Some observers have expressed surprise at the speed and strength with which the New Right positions have established themselves. This day, however, has actually been a long time in coming. It is the result of a 20-year effort that has featured such conservative advocates as Phyllis Schlafly, best known for her opposition to the Equal Rights Amendment, Richard A. Viguerie, who gave the New Right vital help with his direct-mail fund raising, and the Moral Majority's Reverend Falwell.
Using direct appeals that bypass much of the major media, New Rightists have built a well-financed, responsive army of enthusiasts. Recently, Kansas Sen. Nancy Landon Kassebaum joked to New Right leader Sen. Jesse Helms of North Carolina that because of his direct-mail appeals, he writes to the people of Kansas more often than she does.
All this work is now bearing fruit. Republican strategists are hopeful that they can adopt much of the New Right agenda without offending middle-road voters. There is risk in such a plan, but they feel it is not a very great one.
There is also a potentially huge payoff. Tuition tax credits and opposition to abortion hold the prospect of helping the GOP with Roman Catholic voters in areas like the Northeast, normally a Democratic stronghold. School prayer is popular with Protestants in the South, another Democratic bastion.
Besides their knack for good organizing, the New Right is also succeeding because it is riding some important tides in American politics.
Jody Powell, who was press secretary in the Carter White House, says the rise of the right has been a subject of great interest to him.
''I happen to be a believer myself, a Southern Baptist,'' he notes. ''But what is happening here is, in my mind, quite disturbing. It is the consummation of a long set of trends.''
Mr. Powell, however, doesn't single out the New Right exclusively for criticism. Its growing power is the result of other factors. He continues:
''People on the left who are quick to condemn what they now see on the right were less quick to condemn when the cloth and the pulpit were used to support causes closer to their beliefs.'' Vietnam and civil rights were two recent examples.
Further, Powell notes, the breakdown of the family in America has played a role. People looked around them and saw a rise in illegitimate births, abortions , divorces, and pornography.
Powell says a feeling also grew that government and the dominant culture, as portrayed on the television networks, were not just neutral in regard to religion. They actually appeared to hold religious faith ''in contempt.''
That has produced a reaction that Powell calls ''understandable.''
On the other hand, he says, putting doctrinal religious positions into the middle of a political debate causes all kinds of problems. Abortion is one example. Says Powell: ''You cannot have a reasonable political debate if one side views the other side as murderers. That's a conversation stopper.''
As Powell's comments indicate, the rise of the right is now raising concerns of its own. Many religionists, who once were more concerned with winning converts, now try to win political battles. There is concern among some middle-road Republicans, such as Senator Kassebaum, that now, rather than trying to convince people to live more moral lives, the New Rightists will make them do it through law.
Kassebaum says: ''People in the country want to see less government in their lives. That was the appeal of Barry Goldwater and Ronald Reagan. Yet this group wants more government action.''
Political analyst Austin Ranney told an interviewer last week: ''(Reagan) feels that it's not only government's right but government's duty to interfere in people's personal lives in order to uphold morality. Thus, it's good for our children to have religion. Even if their parents don't want to give it to them, the schools ought to make sure they have it.''
Mrs. Schlafly, highly visible at the GOP convention, looked at two of these issues in an interview. On abortion she noted:
''We do believe in government protecting people's life, liberty, and property. ... That's the function of government.''
Protecting the lives of unborn children, she says, is one such proper governmental role, although she feels that on balance, the platform calls for less interference by government on most issues. But if ''husbands are beating up wives,'' obviously that's one place government should act, she says. Abortion is one such issue.
Schlafly observes that there are at least half a dozen versions of a ''right to life'' amendment floating around. The platform mentions no specifics - purposely. A final version, she suggests, might allow for exceptions, such as rape. ''Certainly you have the right of self-defense,'' she adds.
Sen. Jeremiah Denton (R) of Alabama, another ''right to life'' advocate, agrees. Exceptions for situations like rape and incest should be carefully considered, he says.
Prayer in schools also causes concern among many moderates. Whose prayer? they ask.
That should be left to local option, says Mrs. Schlafly. She suggests that a simple prayer such as some people say at grace should offend no one. She notes that the courts have even struck down such prayers as ''God is great. God is good. Let us thank him for this food.''
Could such a prayer hurt anyone? she asks.