President Carter's appointment last week of a personal representative to the Vatican has infuriated the President's fellow Baptists and has touched off a flurry of interreligious strife.

The Rev. Jimmy Allen of San Antonio, newly elected president of Carter's denomination, the 13-million-member Southern Baptist Convention, fired off a telegram to the President charging that the appointment "is in violation of the spirit and probably the letter of the First Amendment to the Constitution." The First Amendment provides for separation of church and state.

Dr. James E. Wood of the Washington-based Baptist Joint Committee on Public Affairs, with a constituency of 25 million Baptists, raised a similar complaint in a telegram of protest to the White House. He added that the appointment of a Vatican envoy "also officially underscores the special concern of this government for one religious body to the point of preferential treatment not accorded any other church of religious body anywhere else in the world."

Similar protests were lodged by an inter-denominational church-state separationist group called "Americans United."

The naming of a Vatican envoy is not a new step, although Carter's choice. Miami attorney David Walters, who will succeed the Nixon-appointed Henry Cabot Lodge, is the first Roman Catholic to be named to the unsalaried post.

But Baptists and other strict constructionists of church-state separation are especially vigorous in protesting the Walters appointment because they fear it signals the upgrading of U.S. representation at the Vatican from its present informal status to full diplomatic recognition of the headquarters of a religion.

Their fears are fueled by the quiet passage last month of an amendment to the Foreign Relations Authorization Act for fiscal 1978. The amendment, introduced by Sen. Richard Stone (D-Fla.), repeals of 110-year-old law, enacted in an era of anti-Catholicism here, forbidding expenditure funds "for the support of an American legation" at the Vatican.

Stone, who is Jewish, said he offered the amendment so that if "some President in the future" wanted to upgrade representation at the Vatican it could be done.

But, he added, "I wouldn't think there is any early or imminent move in the offing in that direction," and denied acting at the behest of the White House.

White House and State Department spokesmen denied knowledge of any plans to change the status of the present informal relationship with Vatican.

President Franklin D. Roosevelt was the first modern-day President to name a Vatican envoy. This was during World War II, when the Vatican was a particularly valuable listening post.

President Truman attempted to name Gen. Mark Clark as a full ambassador, but the outcry from Protestant church groups, spearheaded by Truman's fellow Baptists, forced him to back down.

The United States had no representation at the Vatican until President Nixon named Lodge to the post in 1970. Lodge has continued as the envoy, most recently representing the United States at canonization rites last month for the 19th century American bishop, John Neumanm.

While the Vatican is the international headquarters of a church, it also considers itself a sovereign state, and 89 nations around the world recognize it as such. The United States and Mexico are the only major nations without formal diplomatic ties with the Vatican.

While U.S. relations continue on an informal basis, the Department of States does have a Vatican desk, and maintains what an official described "as a very small office" in Rome, separate from the U.S. Embassy in the Italian capital, staffed by a career foreign service officer and secretary.

A State Department spokesman said it has been "very worthwhile" for the United States to have representation at the Vatican, particularly because of its international character. "The Vatican has all kind of ties in places where we have been weak," he pointed out.

We cited the Lebanese situation, southern Africa and problems of Indo-China refugees as recent examples where such ties have been helpful to this country.

Dr. Wood and other Protestant leaders who oppose any representation at the Vatican maintain that such contacts can be handled out of the embassy in Rome. The State Department says this is not possible because of Vatican restrictions.

The Department spokesman said that in an effort to maintain its identity as a sovereign state "the Vatican makes a big point of it that any country that is not accredited [to the Vatican] must make its representations to the Vatican from an office that is physically separate from its [Rome] embassy."

During the 1950s, when there was no such office, he recalled, "the vatican, to make its point, made it hard" for the U.S. embassy in Rome to arrange even relatively simple things such as papal audiences for visiting Americans.

The official representative of the Vatican in Washington, Archbishop Jean Jadot, is concerned almost exclusively with church affairs, although "on race occasion," the State Department spokesman noted, he functions in a diplomatic capacity.

National Catholic News Service, which is an official agency of the American Catholic Church, reported last week that its "vatican sources indicate the Vatican would welcome full diplomatic relations with the United States," but that the initiative for such a move would have to come from this country.

Russell Shaw, information officer for the American Catholic hierarchy, said yesterday that "I can't speak for individual bishops, but I know that the (National Conference of Bishops) hasn't pressured," for the Walters appointment or for diplomatic recognition of the Vatican.

The White House did consult the president the American hierarchy, Archbishop Joseph L. Bernardin of Cincinnati about the Walters appointment, along with Terence Cardinal Cooke of New York and Walter's bishop. Archbishop Coleman Carroll of Miami.