Sen. Daniel Patrick Moynihan's campaign against Soviet taps on telephone conversations of America citizens has unwittingly exposed hidden aspects of President Carter's personality and policies.

When Moynihan (D-N.Y.) criticized the Carter administration on July 10 for following the Ford administration's pattern of ignoring Soviet eavesdropping on U.S. mocrowave telephone calls, the President two days later fired a personal harpoon aimed - irrelevantly - at Moynihan's Nixon connection. At transmitted one word privately - pro. con or in-between - to Moynihan about the Soviet espionage question.

The brings to light two unrelated facts about Carter. First, Pat Moynihan stands high on the list of people Jimmy Carter simply does not like (and views as a potential rival). Second, for all the President's toughness on human rights, he is influenced by apprehensions over the fate of detente that prevail within important parts of the national security bureaucracy.

Actually, Moynihan has been less caustic in critizing the Carter administration that the President's ally Speaker Tip O'Neill or other congressional Democrats. Moreover, his attack on Soviet eavesdropping was not originally intended as criticism of the President.

Rather, Moynihan feared continuation within the Carter administration of the U.S. government's tendency to overlook unacceptable Soviet behavior for the sake of detente. Beyone that, the dangerous official tendenc to explain away provocative activity worried him. Privately, Moynihan sums it up as "an appeasement psychology" among advisers of this and other Presidents.

But Moynihan was unprepared for the President's blunt riposte at his last press conference when he delivered this non sequitor . "Well, Sen. Moynihan, as you know, has been a member of the Nixon administration in the past, in a very high official position. And he's well able to judge the knowledge that was possessed by the administration." In fact, telephone eavesdropping by Soviet "diplomats" in this country completely surprised the senator.

Moynihan attributed the Carter response to the jugular instict of a rough-and-tumble politician. But White House insiders say it goes deeper. "The President just doesn't care very much for Pat," one presidential aide told us. "He's too Northern, too much New York, too much Havard." Less emotionally, another Carter inner circle over Moynihan as a potential rival for the presidential nomination in 1980 second only to California's Gov. Jerry Brown.

What makes this hostility remarkable is that the two men have had little personal contact aside from some join't campaigning in 1976. The President telephoned Moynihan to seek, unsuccessfully, his support for Paul Warnke's confirmation as disarmament negotiator. But Moynihan has spent no private time in the presidential presence, socially or politically.

Thus, the embryonic Carter-Moynihan feud stems not from abrasive personal contact but from an institutionalized, arm's length hostility - somewhat similar to the anti-establishment hostilities Carter carried into the presidential campaign. Reaching the summit of power has not changed Carter's political style all that much.

Of more lasting importance, however, is Carter's obvious irritation with any senator's poking around into the President's conduct in the face of hostile Soviet behavior. Carter was reflecting the view held within his administration that detente, as a fragile flower vulnerable to the icy blasts of truth, must be protected. Besides, some intelligence officials claim that United States gets as much help from such eavesdropping in Moscow as the Russians do here.

But this last point is contradictd by experts inside the government. If all listening in on microwaves were stopped by both countries, the United States would be a clear winner. In particular, these experts fear Soviet eavesdropping on New York City calls gives them economic information useful in manipulating markets.

Like many centrist Democrats, Moynihan felt at first that inbred instincts of a South Georgia farmboy and ex-career naval officer were strong enough to overcome zealous detentists who surround hime. But the President's reaction to Soviet eavesdropping, along with other trends in national security policy, suggests to Moynihan that environment outweighs heredity in influencing a President.

When he called a press conference Wednesday to unveil a bill designed to protect American citizens from foreign espionage, Moynihan mentioned none of these misgivings. Moynihan follows the old rule of many Irish politicians: Don't get mad - get even. The senator will not soon forget the President's crack at his Nixon antecedents. President Carter is flying so high today that it makes no differecen, but on some tomorrow he may find he took on the wrong senator on the wrong issue.