William J. Murray III, now 37, has traveled far from a time more than two decades ago when, as a gawky Baltimore teenager, he was at the center of the landmark Supreme Court test on school prayers. The issues raised in the case never entirely ebbed and now appear to be cresting anew. Congress has begun debate on proposed Constitutional amendments, including one drafted by the Reagan White House, to permit voluntary prayers in public schools. And this is shaping up as a highly emotional issue of the 1984 Presidential election year.

With reservations, Murray favors a school-prayer amendment, a stance at odds with his atheist mother, Madalyn Murray O'Hair, now 64. Mother and son have been estranged for seven years, and subsequently Bill abandoned atheism for evangelism. (O'Hair's younger son, Jon Garth Murray, remains an atheist and is active in his mother's organization, the American Atheist Center.) However, Murray's present position is based less on his own change of heart than on what he insists has been widespread misinterpretation of the 1963 Supreme Court decision in which he was involved.

He was in public school in 1960 when it was fairly customary in the U.S. to begin each day with a prayer. Young Bill, professing atheism, was allowed to stand in the hallway until the prayer was over. If that procedure made Bill Murray uncomfortable, it enraged his mother, who sued to stop the prayers. Ultimately the Supreme Court ruled that young Bill's hallway banishment was a form of coercive pressure and therefore unconstitutional.

Murray contends that this narrow decision meant only that students could not be forced to pray. But over time, he notes with dismay, it has been interpreted by the public as a ban against all school prayers. Meanwhile, according to Murray, the Constitutional guarantee of governmental neutrality on religion has become warped by school officials fearful of costly lawsuits. He cites the example of seven students, all from the same church: "At the school bus each morning they decided to have a little word of prayer. The school officials found out and told them to stop and desist." He also points to his attempt in January to rent a school auditorium in Wappingers Falls, N.Y.: "It was a public assembly open to anyone, but the newspaper there said we were going to talk about God in the building, and that it was against the Constitution. Well, it's not, but they denied me anyway."

Such bureaucratic insensibility, he says, has resulted in a general perception of "governmental hostility toward religion, not neutrality." To redress that imbalance, he regretfully supports the idea of a school-prayer amendment. "It must be done to satisfy the public backlash if we are to have freedom of religion," he argues. "If the Constitution were properly interpreted, then these amendments would be unnecessary."

Laurence H. Tribe, Tyler Professor of Constitutional Law at Harvard, who opposes any amendment, agrees about the Constitution. "The premise that prayer is not allowed in schools," he says, "is a lie. Official, organized prayer is not allowed, true, but kids can pray if they want." Indeed, some legal scholars think that the conflict within the First Amendment might be resolved ultimately by allowing a moment of silence.

Murray sees his challenge as the conversion of atheists and agnostics rather than Constitutional issues. Twice divorced and a recovering alcoholic since 1978, he lives alone in Garland, Texas, near Dallas. For three years he has been an active Baptist (though not a minister), and he now says what his family did was "a criminal act," which has driven him to seek atonement. His vehicle is the Murray Faith Ministries, a nonprofit, contribution-supported religious organization from which he draws a $1,400 monthly salary and for which he traveled 43,000 miles last year as its sole evangelist. He draws on his own experience: "I tell them I have walked in their shoes. And I can tell them they are on a dead-end road leading to sadness, emptiness and an unfulfilled life." Next month Madalyn Murray O'Hair is scheduled to head an atheist convention in Lexington, Ky. Bill Murray plans to be there, too, to conduct counter-rallies.

"I have become peaceful in the last few years," he says. Perhaps, but the explosive religious issues that he once helped to spark remain at flash point all around him.