Amid tumultuous cheers and applause, delegates from 17 of the 20 Latin American republics yesterday voiced their emotional disapproval of U.S. policy in the Falkland Islands crisis.

After a marathon, two-day foreign ministers' meeting of the Organization of American States, the 17 countries formally condemned Britain's "unjustified and disproportionate armed attack" against Argentina, urged Latin America to support Argentine military efforts and called on the United States to stop assisting Britain and to end immediately the sanctions imposed by President Reagan against Argentina.

The scene at the ornate Hall of the Americas in the OAS headquarters, a little more than a stone's throw from the White House, was a stunning reminder that the administration is caught squarely in the cross fire of the eight-week confrontation and faces a mounting danger that one of the principal casualties of the Falklands war could be its campaign to build an inter-American front against communist penetration of the Western Hemisphere.

Indeed, as one Latin American diplomat privately observed, "it was the United States even more than Britain that was in the dock" when delegates to the OAS ministerial meeting were hammering out the resolution that emerged early yesterday. The United States, Colombia, Chile and Trinidad-Tobago abstained from voting on the resolution, which urged an end to what it called "coercive measures" imposed against Argentina by the United States and members of the European Economic Community.

The testing ground for the U.S. drive to turn back the challenge of leftist guerrilla movements is in Central America, some 3,000 miles north of the fighting in the South Atlantic. But the success of the administration's top-priority effort depends on how much support it can marshal among the disparate Latin countries stretching from the Rio Grande to the southern tip of South America.

In the pursuit of this goal, the Falklands situation, as U.S. officials acknowledge with grim understatement, has been "anything but helpful." The administration's hopes of enlisting Argentina as the Latin American "senior partner" in an alliance against hemispheric communism already have been torn to tatters by Argentine bitterness and recriminations that are likely to fester for years to come.

Similarly, as the OAS meeting made clear, the U.S. position toward the Falklands situation has touched raw nerves of anti-Americanism in Latin America and inflamed them to a greater degree than at any time since the U.S. military intervention in the Dominican Republic in 1965.

At a time when most Latin American governments are shouldering each other aside in their rush to express solidarity with Argentina, U.S. policy makers are not likely to find any of them willing to come within shouting distance of initiatives, whether in Central America or other parts of the hemisphere, perceived as having a made-in-Washington stamp.

It is still too early to make absolute judgments about the long-term effects of the Falklands crisis on U.S.-Latin American relations. Many administration officials, while conceding that it might take from six months to two years to overcome the anti-American fallout, insist that the situation isn't as bad as it appears on the surface.

"In the end, every country is a prisoner of its geography and its trade," one official notes. "For every country in Latin America, except Cuba, which is an unnatural case, the ties lead firmly to the United States and Western Europe. They may be mad at us; they may not like us; but sooner or later, they have to face the necessity of coming to an accommodation with us."

Another official makes a different point: "Because Country X disagrees with us on the Falklands doesn't mean it will automatically depart from other policies that are in its interests on other issues. Take Venezuela for example. It is among Argentina's most emotionally inflamed partisans. But it also has many of the same concerns that we do about Central America, and it has pursued policies there that, in many respects, parallel our own.

"It's not likely that Venezuela suddenly will abandon what it sees as its vital interests in Central America and go in another direction just to spite the United States. It may back away from suggestions that it's cooperating with Washington and protest its independence at every opportunity. But, while its rhetoric may be different for a time, the substance of its Central American policy probably will be essentially unchanged."

There is logic to these arguments, but there also are important elements in the Falklands situation that are different from those that figured most prominently in past instances of U.S.-Latin tensions.

Perhaps the most vivid illustration of the difference was provided last Tuesday, during the U.N. Security Council debate on the Falklands, when the foreign minister of Nicaragua showed up to join Venezuela and Panama in a declaration strongly supporting Argentina. Similarly, during the fiery pro-Argentine speechmaking at the OAS on Thursday and Friday, no country was more ardent in its backing for Argentina than Nicaragua.

Yet, a little more than two months ago, Nicaragua's radical leftist Sandinista regime was openly accusing the rightist military junta in Argentina of plotting with the United States to train and supply guerrillas seeking to overthrow the Sandinista government from bases in neighboring Central American countries.

In short, what makes the Falklands crisis unique is that it has provided a rallying point for unity in a region that, although often regarded as monolithic by the outside world, encompasses some very different and usually antagonistic ideological, racial and cultural influences.

This unity is rooted in the somewhat mystical belief that Latin America's development problems are the result of being kept in perpetual bondage to the economic colonialism of the industrial powers and that the region can realize its potential only by asserting its common heritage to shake off outside oppression.

In the current instance, the immediate target is Britain, which is perceived as unjustly maintaining a foreign colonialist presence in the hemisphere through its control of the Falklands. Usually, however, it is the United States that is cast in the dual role of villain and scapegoat. By backing Britain, Washington unavoidably has exposed itself anew to the Latin American tendency to blame its problems on the "colossus of the north."

This undercurrent of anti-Americanism can be detected in such phenomena as the region-wide demand a few years ago for the United States to surrender control of the Panama Canal and in Cuban President Fidel Castro's success in pushing a brand of communism that owes far more to Yankee-baiting than to orthodox Marxist dialectics. But, while Latin ideologues of all persuasions have sought constantly to use anti-Americanism as a vehicle for Latin American unity, more often than not they have been frustrated by the quarrelsome nature of the region's internal relations.

Although none of the region's countries can be characterized with precision, each falls roughly into one of the categories that academicians sometimes call "the three Latin Americas."

There is the Indian Latin America, which extends from Mexico through much of Central America down the Andean spine of South America to the northern borders of Chile and Argentina; the African Latin America of slave-descended plantation societies, which skips from the Caribbean islands to the South American mainland down through much of Brazil, and the white European Latin America, whose main redoubt is the Southern Cone complex of Argentina, Chile and Uruguay.

Except for Brazil and the tiny republic of Haiti, these countries share the language and colonial heritage of Spain. That surface similarity provides the basis for the concept of pan-American unity, but the reality of the region has been one of historical divisions. Some stem from the prejudices of the different racial groups, some from the isolation imposed by vast distances of difficult geographic terrain. There are political rivalries rooted in fiercely individualistic nationalism, territorial disputes that go back to colonial times and, in the postwar period, seesawing struggles between democracy and military dictatorship.

Most past instances of U.S.-Latin American tension have resulted from one or another of these causes. In earlier times, the United States frequently felt impelled to attempt a peacemaker's role in the region's interminable border disputes. One of Washington's main reasons for opposing Argentina's attempt to reclaim the Falklands by force was concern that an Argentine success would embolden several other Latin American countries to make similar moves against weaker neighbors.

More recently, ideology has been the principal problem. That was the case in 1965 when then-president Lyndon B. Johnson sent American troops to the Dominican Republic. The resulting wave of anti-Americanism came largely from Latin American democratic forces that accused the United States of turning its back on democracy and siding with a military regime against a popular uprising that Washington suspected of being under Cuban influence.

Before the Falklands crisis, Reagan's approach to Central America appeared to be setting the stage for a replay of these same tensions. U.S. opposition to leftist forces in places like El Salvador and Nicaragua, and Washington's ardent courtship of military regimes like Argentina, had been leading to strains with many Latin democracies, like Mexico, which regard the administration as too willing to subordinate support for reform to its fear of communism.

For the moment, however, arguments about whether these criticisms are justified have been swept aside by the sudden emergence of an issue that, temporarily at least, has transcended the many divisions and caused Latin Americans to unite in what many openly call a war between the Hispanic and Anglo-Saxon worlds.

Ironically, they have rallied behind Argentina, which traditionally has considered itself more European than Latin American, is disliked throughout the region because of its attitude of arrogrance and superiority toward its sister republics and usually has stood aloof from appeals to bonds of blood and hemispheric solidarity.

That gives rise to suspicions of some cynicism and opportunism in the expressions of fealty to Argentina. But, even when allowance is made for such considerations, U.S. officials are aware of the Latin feeling that the British military campaign against Argentina is an attack on Latin America and that defeat of the Argentines would be a humiliation for all of Latin America.

In the face of this emotion, the administration finds little sympathy for its rationale--that preserving the Atlantic Alliance is of bedrock importance to the security of the free world and that Argentina was wrong in seeking to resolve a dispute by force.

To the Latin Americans, U.S. support of Britain is confirmation that the United States places more value on its ties to Europe than to them. Even U.S. insistence that disputes should not be settled through force is widely seen in Latin America as an attitude typical of a rich, powerful country with a vested interest in preserving the status quo against the claims of the Third World.

Whether the gulf between these perceptions can be bridged, either by finding a way to halt the fighting on terms that will not leave Latin America embittered or by simply hoping that time will be a healer, is still a wide open question. What seems clear for the present is that Reagan's hopes of pursuing his own vision of a new era in U.S.-Latin American relations have been thrown off the rails, and no one knows how or when they are likely to get back on track.