Deepening friction between Zbigniew Brzezinski, President Carter's national security adviser, and Marshall Shulman, the State Department's Soviet expert, is shrouding policy toward Russia in contradictions that deeply trouble major American allies.

"It's making my skin crawl," one administration policymaker told us in describing what he called the Brzezinski-Shulman "hatred." Hatred is surely too strong a word. Nevertheless, the two former intellectual adversaries from Columbia University have been on a descending curve of policy conflict and personal relations ever since Carter entered the White House.

The result has been Carter's dizzying on-again, off-again wavering toward Moscow: hard-line, soft-line, no-line.

Brzezinski, with total access to the Oval Office, pushes his hard line demanding that the Soviet Union be held to account for its worldwide offensive.

Shulman, 11 years Brzezinski's senior, at 62 is the oldest aide brought to Washington by Secretary of State Cyrus Vance. He refuses to react to Soviet depredations in Asia, Africa and the Far East, advising Vance that SALT II and bilateral U.S.-Soviet relations are all that matter.

A strong president with convictions of his own about handling the Soviets could quickly resolve the conflict and force feuding ministers to comply or quit. Carter's inability to do that has astonished foreign leaders from Western Europe, Japan, communist China and elsewhere.

"Where should I go to find out what America's policy is?" a major European foreign-policy leader, here on a recent fact-finding mission, privately asked a State Department official. The reply was totally unsatisfactory.

But the U.S. humiliation in Iran, plus undisguised ridicule of America's inability to protect its embassies or its ambassadors, could change Carter. He could be forced over to the Brzezinski way, at the expense of the Shulman way.

Political developments on Capitol Hill are also relentlessly pushing Carter. Republican leaders, appalled at U.S. reverses, are opening a major campaign to compel Carter to explain his policy toward the Soviets. The more he and his top aides explain, the more public the Brzezinski-Shulman split must become. In the current political mood, Brzezinski's relatively hard line would win hands down in Congress.

Carter will find it difficult to continue not to choose between the two conflicting methods of treating a Soviet Union that is clearly on the offensive. The alternative is further decline in U.S. standing abroad.

As Vance's top adviser on dealing with the Russians, Shulman succeeded many illustrious diplomats, including Averell Harriman, Llewelyn Thompson and Charles (Chip) Bohlen. Each was a veteran of personal confrontations with the Kremlin's leadership. In contrast, Shulman never had held a top policy job; his experience with the Soviet leadership was on an academic level.

Brzezinski and Shulman, as contradictory in temperament as in attitudes toward Moscow, had a long history of disputation over the United States and Russia that friends of both insist was conducted with professorial courtesy at Columbia and, before that, at Harvard. Shulman was the expert on internal Soviet affairs; Brzezinski the expert on the Soviet world role, its regional political goals and the postwar expansion of its military capabilities.

Once arrived here, however, Brzezinski had the far more prestigious position. But his access to the president did not give him a decisive edge over Shulman in the power struggle. On the contrary, Shulman often has prevailed, thanks to Vance's unflinching support and Carter's unwillingness to overrule his secretary of state.

A case in point, which we mentioned last week, was Shulman's veto of a stiff U.S. rebuke to Moscow for inflammatory anti-American Soviet broadcasts into Iran during the revolution. The Iran "working group," composed of mid-level diplomats, unanimously recommended the rebuke; Vance upheld Shulman's decision not to affront the Kremlin.

Stark new evidence of America's decline and the fears it has unleashed among U.S. allies would seem to require a Brzezinski-Shulman showdown. Without it, Carter cannot begin to persuade his allies that he really knows how be wants to deal with Moscow.