A debate with strong religious overtones swept the United States in 1954 when the words ''under God'' were added to the Pledge of Allegiance to the Flag. Similar debate may follow two proposals now being made by President Reagan: federal tax aid to private and parochial schools and restoration of prayer in public schools.
School prayer was banned by the US Supreme Court in two decisions in 1962 and 1963. The court ruled that such prayer violated the First Amendment requiring separation of church and state. The prospect of passing constitutional amendments to achieve the two Reagan goals is considered uncertain.
Like eight presidents before him, Mr. Reagan, in compliance with congressional mandate, proclaimed May 6 as a National Day of Prayer. Disputes over the relationship of church and state that have torn some countries apart have been less destructive in the United States, but there is an undercurrent of controversy. Now Washington observers are asking whether Mr. Reagan, based on his past positions and statements, plans a more activist attitude. Two developments raise the issue:
* On April 15, the President told the annual convention of the National Catholic Educational Association that he plans to ask Congress to phase in tuition tax credits for private and parochial schools starting in 1983. After three years the credit would reach a maximum of $500 per child; the size of the credit would depend on family income and families would be ineligible above a certain income.
* Mr. Reagan also favors a constitutional amendment to put prayer back in public schools. Evangelist Jerry Falwell, head of the religiously oriented political action group Moral Majority, says that Mr. Reagan will push this as he did in the election campaign, when he wooed many religious groups into his camp. ''We will give it our whole-hearted support . . . as long as the key word is 'voluntary,' '' Mr. Falwell said here in preparation for the White House ceremony. More than 100 people ''interested in prayer'' will attend the Rose Garden gathering, a White House spokesman announced.
The 1980 GOP platform included a plank ''to restore the right of individuals to participate in voluntary, nondenominational prayer in schools and other public facilities.'' It also declared, ''Next year a Republican White House will assist, not sabotage, congressional efforts to enact tuition tax relief into law.''
President Reagan vigorously supported the prayer and tuition tax credit proposals during his election campaign.
Because tuition tax credits would add to federal deficits, the nation's governors at the National Governors Conference voted to oppose them for elementary and secondary schools. Albert Shanker, president of the American Federation of Teachers, also calls for all-out opposition.
By contrast, spokesmen for Roman Catholic schools, which instruct 65 percent of all students not enrolled in public schools, on March 25 urged Mr. Reagan to give ''strong and immediate support'' to tax credits.
In a telephone interview, Joseph Conn of Americans United for Separation of Church and State said his organization opposes tuition tax credits and prayer in schools. He forecast failure for both proposals.