WASHINGTON — The conservative Virginia Baptist and the liberal Massachusetts Catholic are the odd couple of the evangelical-political circuit.

But, as their second forum on moral, ethical and governmental issues showed Tuesday, a funny thing happened to Moral Majority founder Jerry Falwell and Sen. Edward M. Kennedy on their way to the National Religious Broadcasters' 42nd annual convention: They became friends.

During their genteel confrontation, the unlikely pair delineated sharp differences on such issues as abortion, U.S. policy toward South Africa and the role of religion in politics. But they disclosed also that they like each other's families, pray together and enjoy being dinner partners.

Not incidentally, that friendship might be helpful to both men in gaining entree to the rival's philosophical camp.

For example, the encounter Tuesday, a breakfast attended by 2,700 convention delegates, was broadcast live by Cable News Network and was fed to 6,900 cable TV systems with a potential audience of 31.4 million viewers.

Falwell sat to the left of Kennedy and spoke after him. The tone of the session was set when moderator Cal Thomas, communications director of the Moral Majority, introduced the pair as the "traveling road show of the 'Odd Couple.' "

To the delight of the conventioneers, Thomas quipped that the two could easily become a 1988 presidential ticket and that the only remaining decision was "who's going to be No. 1 and who's going to be No. 2."

The quasi-debate format allowed each man to speak for about 25 minutes, and Kennedy used part of his time to make a vigorous attack on racial separation policies in South Africa, which he recently visited. In turn, Falwell--who also has visited South Africa--responded with an impassioned assertion that "major changes" have taken place there, including the opening of some public places to blacks.

Falwell fired his customary shots at abortion and voiced conservative hopes that President Reagan will appoint new Supreme Court justices, forming a "pro-life court" that will reverse the 1973 decision making abortion legal.

Evident Warmth

However, more striking than their well-known differences on social issues was the warmth with which the two men spoke of each other.

Kennedy said that he and Falwell "have come to see each other not merely as opponents but as fellow human beings who know the hopes, the tears and the laughter of life."