Soviet policy makers seem to be taking a new, more sophisticated approach to wooing Western antinuclear advocates. In the process, the Russian Orthodox Church gets a potential boost.
Signs of this emerged from last week's Moscow conference of ''World Religious Workers for Saving the Sacred Gift of Life from Nuclear Catastrophe.'' Meanwhile , the Rev. Billy Graham, invited here as an observer, made statements that puzzled a number of Westerners, including many of his strong supporters.
Dr. Graham, his aides explained, was intent on being a good guest. On departure from Moscow, the American evangelist seemed to explain why: he wants to return to the Soviet Union and preach ''from Siberia to the Black Sea.'' Should the Soviets permit this, they would be making a stunning departure from past policy on religion.
Dr. Graham was a good guest indeed. Asked on various occasions by foreign reporters whether he thought there was freedom of religion in the Soviet Union, he explained that the term was relative. But, he said, in a sense, churches in the USSR were healthier than in the US, and freer than in Britain.
Dr. Graham did preach once, as well, telling a jam-packed Baptist church that God could make the faithful better workers, more loyal citizens, ''because in the 13th chapter of Romans, we are told to obey the authorities. . . .''
The American visitor's behavior perplexed other Western clerics in town for the antinuclear conference, at least some Russian religious figures, and even a few Soviet officials, although this last group made it clear they didn't mind his performance in the least.
But the Soviet news agency Tass and other official news outlets made little of Dr. Graham's apologia for the authorities' attitude toward religion.
The priority issue for the Soviets last week was nuclear arms limitation. The priority audience appeared to be the antinuclear movement in the West. The priority forum: the Moscow conference.
The week-long meeting produced a formal ''appeal'' to world governments that, to many foreign observers, was surprising in its degree of evenhandedness toward East and West. The Kremlin, almost surely, was not surprised.
Although the conference began on a predictably pro-Soviet note, promptly reemphasized by a Syrian and a Sri Lankan delegate, a small group of American clerics then spearheaded a Western bid to prevent a mere one-sided condemnation of Reagan administration arms policy. The Americans, particularly Lutheran presiding Bishop David Preus of Minnesota, are said to have made it clear they would walk out if spurned.
The communique suggested by the Russian delegates, according to conference sources, endorsed the Soviet position on European nuclear forces and, in effect, called on the West to recognize how reasonable the Soviets are. But when American delegates demurred, changes were made. The final product was not completely evenhanded. The conference decried production of a neutron weapon and the ''doctrine'' of limited nuclear war - both items high on the list of Soviet indictment of US arms policy - but included no specific criticism of any Moscow weapons system.
Still, the final document's paragraph on general disarmament issues and proposals was redrafted in distinctly non-Tasslike fashion. Gone was the call for the West to reciprocate Soviet missile initiatives. In place of kind words for the nuclear freeze proposals of US Senators Edward M. Kennedy (D) of Massachusetts and Mark O. Hatfield (R) of Oregon was a pat on the back for Ronald Reagan: ''We also welcome the expressed readiness of the United States to conduct formal negotiations on the reduction of strategic nuclear arms beginning as early as next month.''
''We see hope in recent expressions on both (the Soviet and American) sides of a willingness to meet each other and to negotiate . . . ,'' the communique continued. ''We would, however, appeal still to the Soviet Union, to the United States, and to other nuclear powers, to hasten the pace of implementing programs of disarmament.''
Tass, in its English-language service, quoted these passages of the conference appeal. Domestically, the official media made only cursory mention of the contents.
Observers say it is unthinkable that Russian religious figures at the conference would have accepted the redrafting without a nod from secular Soviet authorities. But Western delegates saw a number of signs that the Kremlin, moreover, may have expected and even encouraged such an outcome from the start.
For one thing, the composition of the conference's ''drafting committee,'' including two American and two West European delegates, made some bargaining at least possible. Too, a speech at the meeting by Georgi Arbatov, a ranking Soviet party official and the Kremlin's best-known adviser on US affairs, generally steered clear of explicit condemnation of Reagan arms policies, in favor of a more restrained and balanced tone.
The feeling of many Kremlin-watchers here is that Soviet authorities decided they had much more to gain from a conference that yielded a communique credible in the West, than by trying to push through an endorsement of Soviet policies at the risk of breaking up the meeting.
Late last year, a veteran ideological authority and member of the Soviet Politburo, Boris Ponomaryov, wrote an article calling for an ''all-embracing (world) antiwar coalition that would include the activities of the broadest possible strata of the population, the widest possible range of political forces.''
Western religious groups might fit the bill. Moreover, some diplomats note, the Russian Orthodox Church can probably act more credibly to encourage Western antinuclear sentiment than can secular Soviet politicians.
If this is the strategy, Moscow will presumably begin to seek increased overseas action by this nation's officially controlled church organizations.
Remarks by Russian clergymen and from Soviet officials suggest the process would amount to a marriage of convenience for the state, and of necessity for the church.
The church's evident hope is that in winning a more important role in Soviet diplomacy, it may secure an inch-by-inch expansion of prerogatives at home.