The angry dispute between U.N. Ambassador Jeane J. Kirkpatrick and Secretary of State Alexander M. Haig Jr. over the Falklands crisis has underscored anew the tensions between foreign policy pragmatists and ideological hard-liners competing for influence with President Reagan.

That was the private assessment yesterday by administration sources embarrassed and dismayed by Newsweek magazine's revelation, on the eve of Reagan's departure for the European summit, that two of his top foreign affairs experts had exchanged recriminations over the telephone last week.

The sources, who stressed there is no expectation that Kirkpatrick will resign over the incident, noted that part of the problem stems from personality factors that have caused Haig and Kirkpatrick to rub each other the wrong way almost from the beginning and that, on at least two earlier occasions, led to highly publicized disputes between them.

A year ago, some of Haig's aides caused acute embarrassment to the White House when they intimated to reporters that Kirkpatrick had mishandled delicate U.N. negotiations aimed at softening moves to censure Israel for bombing Iraq's nuclear reactor. Then, early this year, Kirkpatrick came close to resigning to protest what she regarded as Haig's unwillingness to antagonize America's European allies by pressing for strong measures against the military crackdown in Poland.

But, the sources also acknowledged, as the disagreement over Poland made clear, there is an ideological content to the disputes that goes beyond personality conflicts.

That involves the gulf between the relatively moderate and pragmatic approach to foreign relations advocated by the Haig-led State Department and the administration's more hawkish element, symbolized increasingly by Kirkpatrick, that wants a militant and consistent anti-communism at the core of all policy decisions. Even in an administration whose basic instincts are clearly right of center, these two warring strains have been evident from Reagan's first days in office.

In recent months, the more moderate Haig faction has emerged as dominant. But as the latest Haig-Kirkpatrick square-off demonstrated, the so-called "neoconservatives" are still waging a rear-guard action hoping to gain the upper hand eventually in administration policy councils.

In that respect, the Falklands crisis and the U.S. "tilt" toward Britain seemed an almost inevitable battleground.

Kirkpatrick, who wrote her doctoral dissertation on Argentina and thus regards herself as the administration's leading expert on Latin America, is perhaps best known for advocating that the United States must ward off the threat of "totalitarian" communist states in the Western Hemisphere by aligning with "authoritarian" military regimes such as the ruling junta in Argentina. Ironically, that idea has the general support of Haig, whose first experience in foreign affairs was in planning campaigns against Latin guerrilla forces during the 1960s and who also considers himself a Latin America expert.

But, when it came to a showdown between Argentina and Britain, Haig reluctantly but firmly came down on the side of those who argued that the bedrock priority of U.S. policy must be to avoid ruptures with Britain and other European allies whose estrangement could destroy the Atlantic Alliance. It was this policy that caused Kirkpatrick, in a 45-minute phone conversation, to charge, according to the Newsweek account, that Haig and his key advisers were "Brits in American clothes . . . totally insensitive to Latin cultures."

She also is known to have pressed her view during a meeting Monday with Reagan that the United States must seek to repair damaged relations with Latin America by returning to a more neutral stance. The sources said the meeting, which was at Kirkpatrick's request, had been scheduled before the Newsweek article came out and was concerned more with her setting forth her policy ideas than with rehashing her argument with Haig.

Following the meeting, Kirkpatrick was understood to have told aides that she had no plans to resign, that she believes Reagan agrees with her on the larger implications of the Falklands situation and that she considers the debate over U.S. policy direction as far from decided. But, while that was a sign the internal guerrilla warfare is likely to continue, many sources said they doubt the administration has any option other than to continue backing Britain.

The sources also said Kirkpatrick's action in going directly to the president was the sort of tactic that frequently has annoyed Haig in the past and, more recently, national security affairs adviser William P. Clark, who is responsible for maintaining harmony within the administration's policy-making apparatus.

On the other side, Kirkpatrick, a Democrat who split with her party because she regarded its positions on East-West questions as overly soft, has chafed continually at what she considers Haig's efforts to cut her out of policy decisions and consign her to an essentially figurehead role.

During the first stages of the Falklands crisis when Haig sought to mediate a solution, Kirkpatrick is known to have spoken critically to U.N. colleagues about his shuttle diplomacy. Later, when the mediating effort shifted to U.N. Secretary General Javier Perez de Cuellar, Kirkpatrick was understood to have become annoyed when Haig made known his doubts about chances for a successful U.N. solution.

U.N. sources said she made no effort to disguise her belief that Perez de Cuellar was a more skilled and understanding mediator than Haig and that, even after the United States supported Britain and criticized Argentina as an aggressor, she continued to maintain friendly contacts with Argentine diplomats.

At the State Department, that was regarded as an annoying reminder of the administration's embarrassment when Kirkpatrick, on the day of the Argentine invasion, was guest of honor at a dinner given by the Argentine ambassador here.