The first casualty of President Reagan's decision to side openly with Britain in the Falkland Islands dispute is his hope of enlisting Argentina as a key ally in the U.S. campaign to build an inter-American front against communist penetration of the Western Hemisphere.

As one of Latin America's major military powers, Argentina has figured prominently in the planning of U.S. policy makers, who viewed it as playing a potential, "cutting-edge" leadership role in strategic ventures ranging from naval vigilance over the South Atlantic to the support and training of anti-communist forces throughout Central America.

In addition to the almost certain loss of Argentine cooperation in this high-priority effort, Reagan's "tilt" also is likely to affect U.S. relations with the rest of Latin America by causing major ripples in the Central America-Caribbean region that is the principal testing ground of Washington's drive against leftist guerrilla movements.

In its most immediate and obvious form, the fallout probably will involve a rush by Latin American governments to express their solidarity with Argentina and to either denounce the United States or adopt an attitude of coolness toward any initiatives that bear a made-in-Washington stamp.

However, as Argentina learned to its dismay during the Organization of American States meeting here last week, this solidarity does not extend beyond fiery rhetorical flourishes. Once the obligatory bows have been made to the principles of inter-American brotherhood and non-intervention in the hemisphere, there is little chance of Latin America rallying behind Argentina to try to punish the United States.

Instead, the real danger to U.S. policy goals is that the Falklands crisis will cause various realignments in the balance of political forces within Latin America that are likely to leave the Reagan administration increasingly isolated as it searches for allies willing to lend either concrete or moral support to the policies it is pursuing in Central America.

Although such factors as sub-regional rivalries play important roles, the key characteristic of internal Latin American relationships centers on the interplay between the area's democratic and military regimes. And, where Central America is concerned, most of the Latin democracies have taken positions that veer sharply away from the main lines of U.S. policy.

That is especially true of Mexico, which is the dominant power in the northern part of the region and which exercises great influence throughout the Caribbean basin.

In marked contrast to the hard-line U.S. approach, Mexico has shown marked sympathy for the leftist guerrillas in El Salvador and has sought to prod the United States toward negotiation with the insurgents there and with Nicaragua and Cuba, the two countries that Washington regards as the wellsprings of subversion and insurgency in the area.

During recent weeks, these divergences have caused an increasingly ill-disguised chill in U.S.-Mexican relations. In fact, the current U.S. foot-dragging on getting into talks with Nicaragua stems, to a considerable degree, from Washington's belief that Mexico is too sympathetic to the revolutionary Sandinista regime in Nicaragua and its resultant reluctance to accede to Nicaraguan calls for holding negotiations under Mexico's mediating auspices.

With most of the democracies either following Mexico's lead or standing aloof from the Central America situation, the administration, from its first days in office, has been compelled to look for support from the military-dominated regimes on the other side of the political spectrum.

In this, it has been influenced strongly by Secretary of State Alexander M. Haig Jr., whose views on Latin America were shaped by his experience in helping map Latin American counterinsurgency campaigns during the Kennedy administration; by the Pentagon, which long has been anxious to reestablish its once close ties with Latin military establishments, and by such ideologically influential Republicans as Sen. Jesse Helms of North Carolina, who regard the Latin military as a reliable bulwark against communism.

The result was an abandonment of the activist human rights policies of the Carter administration in favor of a broad-gauged effort to cultivate close new relationships with military-controlled or influenced regimes ranging all the way from the small republics of Central America to the Southern Cone countries at the other end of the region.

In this scheme, Argentina quickly came to assume special importance. It had a size and weight roughly comparable to Mexico. Its military leaders, after a period of murderously brutal repression in the late 1970s, appeared to be moving toward internal policies sufficiently moderate to turn aside complaints from U.S. human rights advocates.

In short, Argentina's generals, led by the current junta president, Leopoldo Galtieri, seemed both able and willing to play the ideological role marked out for it by Washington.

The Soviet Union's grain purchases might make it Argentina's largest customer, but, as Galtieri assured everyone on a visit here last November, his country was fiercely and unequivocably anti-communist.

Many experts on Latin America have believed from the outset that the idea of Argentina playing a far-ranging role in the hemisphere was seriously flawed. Despite a common language, the distance between Argentina and Central America is vast, not only in miles but also in cultural and racial distinctions.

The Argentines, a strongly parochial, white European people with a habit of referring sneeringly to the Indian and African-descended populations of the Caribbean region as "tropicales" or "tropical types," are widely regarded in the north as racist and arrogant.

In addition to the cultural hostilities that Argentina provokes among its sister republics, its traditional rivalries with Chile and Brazil mean that these countries almost automatically would oppose any attempt by the Argentines to take a leadership role in hemispheric military affairs.

Still, these factors were brushed aside by the Reagan administration in its rush to enlist Argentine support to help train pro-American forces in Central America and, according to persistent but unverified rumors, to take part in mounting covert action activities against Nicaragua.

In fact, the U.S. courtship was so ardent that there now seems to be grounds for assuming that the Argentine generals unrealistically believed that Washington was so keen to win their friendship that it would back their play against the Falklands.

Instead, the relationship has been left in ruins, with the Argentines embittered by what they regard as an American betrayal and U.S. officials like Haig now referring privately to the generals in Buenos Aires as "power-mad thugs."

Whether the rupture is totally beyond repair remains unclear, but it does seem certain that the United States no longer can count on much help from Argentina in Central America.

Nor do the problems end there. Within the OAS, Argentina's most ardent backers have been two important Caribbean countries: Venezuela, which has emotional territorial claims on two of its neighbors, and Panama, which sees British control of the Falklands as analogous to its own former "colonialism" problems with the Panama Canal.

Venezuela had been the only major Latin American democracy to side with the main thrust of U.S. policy in El Salvador. But that support was contingent, to a great extent, on sympathy for El Salvador's Christian Democratic president, Jose Napoleon Duarte.

Now, when the apparent U.S. willingness to drop Duarte as an accommodation to his rightist adversaries has started to cause anxiety in Venezuela, Washington's position on the Falklands could become another reason for the Venezuelans to question whether they want to stay on the same track.

The same problem potentially exists with Panama, which had been moving cautiously toward sharing U.S. concern about Nicaragua, but which might now feel inhibited from doing anything because of U.S. identification with Britain.

Even Nicaragua is expected to exploit its strong defense of Argentina at the OAS meeting by arguing to those military regimes not directly within the Caribbean area that its show of solidarity entitles it to ask for their support against U.S. efforts to penalize them by gaining financial aid from organizations such as the World Bank.