Leaders of the Jewish and Orthodox Christian communities criticized inauguration organizers yesterday for not including a rabbi and an Orthodox priest in the religious segment of the inauguration of President-elect Jimmy Carter and Vice President-elect Walter Mondale.

The decision to have only Protestant and Roman Catholic clerics pray at the ceremony braks with 20 years of tradition. In 1949, a rabbi joined Catholic and Protestant participants for the first time. In 1957, an Orthodox archbishop was inclused in order to give symbolic representation to the four major faith groups in the country.

Inauguration officials announced last week that United Methodist Bishop WIlliam R. Cannon of Atlanta, a personal friend of Carter, would give the invocation and Catholic Archbishop John R. Roach of St. Paul Minneapolis, a friend of Mondale, would offer the benediction.

Isasc Goodfriend, a Jewish cantor from Atlanta, will appear to sing the "Star Spangled Banner" to clse the ceremony.

Inaugural spokesmen said the program reflects the President-elect's wishes.

"A great deal of insensitivity has been shown by the officials," said th Rev. John Taviarides, pastor of St. Sophia Greek Orthodox Catheral in Washington. For several weeks he has been trying to persuade inauguration officials to place Archbishop lakovos, head of the Greek Orthodox Archdiocese of North and South America, on the program.

Archbishop lakovos has prayed during the last four inaugurations as a representative of the 6 million Orthodox Christians (Greeks, Russians, Syrians, Serbs and others) in the nation.

Orthodox churches, which pride themselves as preserving the faith from the time of Christ's Apostles, do not consider themselves either Protestant or Catholic and have a separate representation in the National and World Councils of Churches.

"We're very unhappy about it," said Father Tavlarides. "Our people were looking forward to it. To them, it was a sign that we had come of age in America, that we were no longer an immigrant group, but a major faith in this country. It is a source of pride for immigrants and their children and grandchildren to see their archbishop offer a prayer for the President of the United States."

Rabbi Mare Tenenbaum, ecumenical officer for the American Jewish Committee in New York, said that, as planned, "the emphasis will come through that this is only a Christian nation."

"It will be seen as a message that Orthodox Christians and Jews are not part of the business of America," he said.

"A cantor singing the 'Star Spangled Banner' is a sop to the Jews. It will be seen by some as a joke."

Both men noted that having a cantor sing the national anthem mixes religion and patriotism in a way distasteful to many people. They also expressed concern that the time is ripe for a national civil religion to be imposed on the country.

Bradyl Tirana, cochairperson of the inaugural committee, said the "President-elect wanted a simple and traditional ceremony." The "history of past inaugurations" was made available to Carter and Mondale, he added.

Before the second inauguration of President Franklin D. Roosevelt in 1937, no minister took part in a swearing-in with the exception of the day George Washington entered office.

As Rabbi Tenenbaum noted, the symbolic religious representation has occasionally "gotten out of hand."

In 1961, at President John F. Kennedy's inauguration, the invocation of Richard Cardinal Cushing of Boston lasted at least five minutes.

And in 1969, President Richard M. Nixon asked five religious leaders to invoke God's blessings for his first administration.