Washington — Will the United States become the 108th country to establish diplomatic relations with the Vatican? This is a strong possibility as the US Congress moves to repeal an 1867 law that prohibits the federal government from spending money for a diplomatic mission to the Vatican. The move is in the form of an amendment to the State Department authorization bill. Virtually unnoticed, the amendment has already passed the Senate by unanimous consent. It will soon be taken up in a House-Senate conference where, according to congressional sources, it has a good chance of being approved.
President Reagan has made no public mention of the issue. The administration is not actively supporting the Senate effort to clear the way for a change of US policy. But White House officials say the President generally favors the amendment, seeing in it some foreign policy advantages.
Appointing an ambassador to the Vatican would have enormous domestic political advantages for Mr. Reagan. Assuming he runs for reelection, the President will be courting the votes of labor and Roman Catholics, and an overture to the Vatican would be one way of doing this. In fact, the wooing seems to have begun. On his way home from China, Caspar W. Weinberger stopped off to meet with Pope John Paul II, becoming the first US secretary of defense to meet with a pontiff in the Vatican.
Political observers also note that Reagan feels a special affinity for the present Pope, not only because of the latter's political role in Poland, but also because the two leaders share the experience of an assassination attempt.
Protestant and Jewish church groups, however, are vigorously protesting the congressional action. They view it as a breach of the constitutional principle of separation of church and state. The National Council of Churches, Baptist Joint Committee, National Association of Evangelicals, and several other organizations held a press conference at the Senate on Wednesday to voice their opposition to the legislative amendment.
''This is not a knee-jerk anti-Catholic reaction, but a commitment to religious freedom,'' commented Gary Ross of the General Conference of Seventh-Day Adventists in a telephone interview. ''The amendment would be a great affront to religious liberty, to the First Amendment, and to the church-state separation as it has worked out in the American environment, which means government neutrality to religion.''
If approved in House-Senate conference, the amendment would not automatically lead to setting up a US mission at the Vatican. The legislation is merely advisory. It would be up to the President, who constitutionally appoints ambassadors, to act or not act on the congressional recommendation. But Reagan could come under intense political pressure to follow through.
Some State Department officials also favor the move. They note that, if relations with the Vatican were formalized - and the President does have a personal envoy to the Holy See - this would not be with the Pope as a religious leader but as a chief of state. This, they say, would offer better channels for exchange of information with the Vatican, which has tremendous influence and contacts throughout the world.
Sen. Richard G. Lugar (R) of Indiana, sponsor of the amendment, has criticized the ''awkward charade'' of the present situation in which American presidents have maintained personal representatives to the Vatican without formal diplomatic ties. It is only ''practical'' to regularize relations, he told the Senate last month.
The Polish question has loomed large in Senate thinking. Sen. Dan Quayle (R) of Indiana, one of the cosponsors of the amendment, applauded the Pope's ''successful intervention with Polish leaders'' on behalf of the people of Poland.
''Under the courageous leadership of Pope John Paul II,'' Senator Quayle said on the Senate floor, ''the Vatican state has assumed its rightful place in the world as an international voice. It is only right that this country show its respect for the Vatican by diplomatically recognizing it as a world state.''
More than 100 countries now have diplomatic missions at the Vatican. Britain established formal relations last year, and Nepal recently became the 107th nation to do so.
Historically, the US has maintained formal diplomatic ties for only a brief period: 1848 to 1867. The prohibition against funding of a ''legation in Rome'' was passed at a time when the Vatican began losing its papal states to the Republic of Italy. In the recent period, Presidents Roosevelt, Truman, Nixon, Ford, Carter, and Reagan chose to have personal envoys to the Holy See, mindful of the domestic political benefits of such a policy. In 1951, Mr. Truman tried to establish formal ties but was blocked by a public outcry. A similar congressional move in 1977 also failed.