In the worsening crisis over the Siberian natural-gas pipeline, the United States and Europe are fundamentally at odds on two policies crucial to the Western alliance: how to deal with the Soviet Union; and how to protect their national economies, all of which are feeling the pain of prolonged recessions.

Damage to the alliance, as seen from here, is by no means confined to the events of last week, when the United States imposed sanctions on two French companies for defying President Reagan's ban against shipping equipment for the pipeline.

"This problem is continuing to grow with no sign of a solution," a senior member of the British Cabinet said Friday.

Shipments scheduled to be made this week will put British, German and Italian companies in the same position of violating U.S. regulations as the French companies already punished by the administration.

The roots of the dispute, however, long predate Reagan's restraints last winter on supply of U.S. technology for the pipeline as a punishment to the Kremlin for martial law in Poland. They date at least to the economic disruptions caused by the massive oil price increases of the mid-1970s and the collapse of Soviet-American detente as the decade drew to a close.

In response to the threats posed by those two developments, the interests of the United States and its Western partners appear now to have openly split.

There have been the serious alliance tensions over development of the neutron warhead to be placed in Europe and, later, U.S. plans for the deployment of medium-range nuclear missiles on the continent. In addition, the United States and its partners have differed sharply on the use of trade sanctions as a weapon, not only against the Soviets, but also against Iran after the seizure of American hostages there in 1979.

The economic scourges of inflation, unemployment and high interest rates that stem from the time of the oil jolts, have heightened political sensitivities in all the countries. Moreover, as in the pipeline tangle, economic and security or defense matters have become intertwined, rendering the difficulties harder to understand, let alone resolve.

In the opinion of diplomats and officials in European capitals interviewed in recent days, the net effect of all these troubles has been to accumulate grievances across the Atlantic and reduce the sort of mutual trust basic to the compromises that sustain an alliance of democracies.

For instance, American appeals six or seven years ago for the allies to reduce their dependence on oil from the Organization of Petroleum Exporting Countries were a major factor in their turn toward the Soviets for energy supplies.

In time, pipeline contracts between the Soviets and U.S. and European companies came to represent the largest East-West commercial transaction in history. By some estimates, Soviet profits from the deal will reach $10 billion a year after 1985.

But while trade relations across the blocs went forward, the political climate between Washington and Moscow deteriorated, especially after the Soviets invaded Afghanistan in 1979 and the Senate failed to ratify SALT II, the strategic arms accord.

Successive American administrations placed an increasing premium on improving NATO's security position. The Reagan administration in particular has given top priority to upgrading Western defenses and, for the first time, has made what amounts to economic war on the Soviets a major element of its strategy.

All four of the European governments involved in the pipeline controversy -- Britain, France, West Germany and Italy -- generally share the administration's sentiment for taking a consistent and firm line with the Soviets and favor improved Western defense, even in the controversial area of nuclear weaponry.

But, as their defiance of Reagan on the pipeline equipment shows, all strongly dissent on the president's tactics in key instances.

The president's proposals for deep reductions, made at the Geneva talks with the Soviets on strategic and intermediate-range nuclear weapons, have substantially lessened any official criticism of U.S. plans for a defense buildup.

But the public's feelings on the matter still run high as Defense Secretary Caspar W. Weinberger acknowledged when he felt it necessary to address a detailed letter to European newspaper editors denying that the United States was preparing to "wage protracted nuclear warfare."

Moreover, as the 1983 date for deployment of the medium-range missiles draws closer with no discernible signs of progress in the Geneva talks, European officials believe that suspicions will be revived about the seriousness of American intentions in the arms talks.

For now, the president's main troubles are in the economic area. Europeans are baffled that Reagan does not recognize the degree of resentment caused by American insistence on selling huge amounts of grain to the Soviets while demanding that others make trade sacrifices.

"Our jobs are as important to us in this time of unemployment as your farmers are to Reagan," one official said after the United States agreed this month to extend the Soviet-American grain sales agreement another year.

Diplomats and virtually every major periodical in the countries involved, across the political spectrum, are skeptical of the president's distinctions between the sale of grain, which takes hard currency from the Soviets, and the proposed purchase of gas, which will give the Kremlin a major new source of cash. They also say that the Soviets will build the pipeline anyway, just as they found grain when then-president Carter embargoed it after Moscow's intervention in Afghanistan.

Even more decisively, Europeans, including such supporters of the president as British Prime Minister Margaret Thatcher, resent Reagan's effort to impose extraterritorial authority on foreign-based companies by ordering cancellation of contracts.

In directing four British companies to ignore the U.S. ban this month, the British trade secretary, Lord Cockfield, said, "The application of American law outside United States jurisdiction is unacceptable."

The loss of pipeline deals would cost Britain 2,000 jobs, according to official estimates, at a time when unemployment is approaching 14 percent. The situations in France, Germany and Italy are similar.

In other words, the Europeans' adamant stance arises from their objection to the principle of Reagan's ban and to its practical effect on each of them. With a raging dispute over European steel exports, on which the United States is levying heavy new duties, and lesser problems in agriculture and textiles added in, the trade and economic climate in the alliance is plainly not conducive to either side's giving in.

On the political front, Thatcher and her counterparts in France, Germany and Italy believe that the only winner in the pipeline crisis is the Soviet Union, which sees the allies fighting among themselves. "That alone might keep the Kremlin from easing up on Poland," a top British government official said.

The spectacle is precisely the reverse of what is needed to meet the Soviet challenge in all areas, diplomats contend. "I find it difficult to believe that Reagan will not come to understand that himself," said one senior diplomat.

European officials say that what has already happened in the pipeline saga cannot be erased, but the president, who they concede is the most powerful figure in the Western world, should reassess his position to protect the alliance.

"He's shown the Soviets he was serious about doing what he could to stop the pipeline," one official remarked. "We've kept our contracts. Now let's move on before it's too late."