While organized labor has been throwing rolling pins at the Republicans over domestic policy and working feverishly to defeat President Reagan, conservative Republicans have been blowing rhetorical kisses and hard dollars right back at an obscure unit of the AFL-CIO.

The object of these affections is the labor federation's far-flung, sometimes heroic and staunchly anti-communist foreign operation.

Organized labor's arch foe, Senate Labor Committee Chairman Orrin G. Hatch (R-Utah), is battling to raise the operation's federal funding.

It is being touted by Hatch and administration officials as a skilled evangelist for the American way abroad and has been put in charge of a government program for visitors to the United States. And it has contributed its own chief as a policy adviser to the White House on a major foreign hot spot.

The AFL-CIO worldwide "has tremendous leverage for political activity compared to, say, CIA covert operations, which often fail," a Hatch aide said. "The AFL-CIO in general takes foreign policy positions to the right of Ronald Reagan."

Recently, for example, the AFL-CIO managed to delay briefly a Reagan administration move to relax U.S. economic sanctions against Poland. AFL-CIO President Lane Kirkland rapped the administration for faltering in its resolve against the Soviet-backed imposition of martial law there.

Hatch, a nemesis of organized labor in the United States, "did considerable soul-searching before he decided to deal with the devil" of organized labor, his aide said. Now Hatch is fighting for what he calls "the first money for the federation's foreign political operations since the CIA scandals of the 1960s," when it was revealed that labor organizations had accepted money from the intelligence agency.

"It is a fascinating political fact that there is an inverse relationship between the domestic posture of an administration toward labor and its posture on foreign policy," said Robert W. Searby, deputy undersecretary for international affairs at the Labor Department. "And it's happening now in spades."

This cross-alignment at the least puts an asterisk on the AFL-CIO's unprecedented embrace of the Democratic Party as the 1984 election year nears. Economic and job concerns may unite many union voters behind a Democratic presidential suitor but, when it comes to foreign affairs, Republicans have a patented courtship routine, replete with flags and fireworks, that has won working-class hearts.

The relationship between labor and Republicans in power is ironic but not surprising in light of history; nor it is simple. The two do not see eye to eye on foreign policy everywhere, and labor's ranks have been divided bitterly on the subject. In the scrambled political landscape of El Salvador, for example, labor's posture has moved, after internal wrangling, to the left of administration policy.

Government officials said the AFL-CIO's foreign operatives, far from being anybody's tools, obstinately insist on doing things their way no matter whose money they accept. Moreover, their activities go beyond simple anti-communism.

Irving Brown, Kirkland's enigmatic ayatollah for foreign operations, said the labor movement looks to only one beacon to chart its course among dictators, coup-plotters, strongmen, guerrillas and factions:

"We support trade union forces, period," he said.

Said the Hatch aide: "There's nothing more authentic than a trade union that's been in a country for 30 years . . . . What we are doing is getting taxpayer money for a public, overt foreign policy instrument, operated by private citizens."

Some persons across the ideological spectrum criticize labor's tactics, methods or motives in one country or another. But there is little dispute that its field network for decades has been an important ex officio arm of U.S. government policy.

Of particular value in Third World countries, labor representatives often have the only mass organization and, over the decades, organized labor has been the American institution most directly challenged by communists.

The U.S. Foreign Service has institutionalized the government-organized labor relationship by staffing its overseas posts with labor attaches. In the late 1960s, some unions acknowledged receipt of CIA funds for postwar rebuilding of the European labor movement. Through the upheavals of the Vietnam war, the AFL-CIO under the late George Meany backed government policy down the line.

"The less socially progressive and labor-oriented an administration is, the closer it is likely to be to labor's anti-communism," an administration official said. "Beyond that, when you have lousy domestic relations you look for a bridge elsewhere, something you can talk to each other about comfortably and something you can fund."

A labor official, confirming the dichotomy, repeated a sentiment currently in use by labor's presidential candidate, former vice president Walter F. Mondale, in his campaign speeches: "There's a type of conservative who loves free trade unions overseas but is less than enthusiastic about their role in domestic affairs."

Accordingly, Hatch, working with AFL-CIO's Brown, has become "labor's sugar daddy" for foreign programs, as one administration official put it.

Hatch backed increases of $6 million for fiscal year 1984 for new foreign labor projects administered through Searby's office at the Labor Department, aides said, although $4 million of the increase was deleted recently by House-Senate conferees.

Hatch also has been among leaders of a broad bipartisan push for $13.8 million in new funds for an AFL-CIO institute to administer the bulk of Reagan's trumpeted Endowment for Democracy program, designed to sell the American way abroad, according to an aide to the House Foreign Affairs Committee. This program would give labor greater flexibility than is afforded by its other federally funded operations, officials said.

The AFL-CIO's main recipient of government funds has been the Agency for International Development. AID has increased its funding from $16 million to $17 million for three AFL-CIO institutes that focus on developing nations.

Charles Z. Wick, head of the U.S. Information Agency, also has cultivated good relations with the AFL-CIO leadership, according to officials. He has awarded the federation a $400,000 contract to take over a foreign visitors program to bring top trade unionists here.

"They can do it better and at less cost" than can the government, USIA's Ron Trowbridge said. "You have to separate domestic politics from international programming . . . . I think it speaks well of us to have the broadmindedness to select the AFL-CIO for this."

A sampler of foreign activities backed by the U.S. labor movement includes providing money to the Polish trade union Solidarity for mimeograph machines, freeing jailed political prisoners in Chile, teaching black South African trade unionists how to organize and generally helping to educate potential leaders in Third World countries.

The AFL-CIO's recent convention in Hollywood, Fla., had the trappings of a mini-U.N. gathering, with simultaneous translations of the proceedings into several languages and a contingent of administration foreign policy officials, plus former secretary of state Henry A. Kissinger and his bipartisan commission on Central America.

There were foreign dignitaries and trade unionists, many of them trained about democracy and trade unionism in AFL-CIO schools. Luis Alberto Monge, president of Costa Rica, the most Democratic country in Central America, was Exhibit A in this category.

The AFL-CIO "has trained more democratic leaders in the hemisphere than all other private and public American institutions combined," the Labor Department's Searby said.

Irving Brown, Kirkland's "secretary of state," runs the labor federation's international operations from an office in Paris, coming to the states only when he has to. Approaching his 72nd birthday, Brown sells democracy like a Fuller Brush man.

Asked in an interview what he thinks about the AFL-CIO's current political pas de deux with the relative soft-liners of the Democratic Party, Brown shrugged.

"I've seen enough of Republicans and Democrats both that sometimes I have to hold my nose," he smiled, throwing in a discourse on the difference between European and American political parties. "Maybe we'll make the Democrats a little better, or maybe they'll make us a little worse."

After World War II, Brown played a key role in foiling attempts by communist-controlled labor groups in Europe trying to disrupt the U.S. economic aid program.

Kirkland appointed Brown head of all AFL-CIO foreign operations in early 1982.

As for the worldwide labor network, it is an acronym soup.

The labor federation operates three institutes with about three dozen American field representatives in Africa, Asia and Latin America, the last being the largest. These elements are funded primarily by AID, with the AFL-CIO contributing as much as 10 percent of the costs.

The federation also participates, despite rocky relations in the past, in the International Confederation of Free Trade Unions, which represents the democratic West with 118 affiliates in 88 countries and a claimed membership of 51.8 million.

The Trade Union Advisory Committee, including unions of 24 countries in the industrialized countries, tries to deal with international monetary fluctuations.

And the Geneva-based International Labor Organization, thanks to the AFL-CIO, boasts more U.S. influence than most international organizations, specialists said. A tripartite body of elected officials, business and labor representatives, it was made a forum by the United States for the debate about human rights abuses in Poland following recent labor unrest there.

Increasingly important to labor as a means of dealing with the proliferating multinational corporations are the more than 16 International Trade Secretariats, sometimes referred to as "multinational unions." They unite workers on the basis of their craft, industry or occupation, and their worldwide membership is said to be more than 53 million.

That they can overcome conflicts in ideology, lack of a legal framework and other barriers to bargaining across international borders is unlikely, experts said. But efforts are being made to increase the international flow of bargaining-oriented information and help in establishing contacts with multinational parent companies.

With roots stretching to the teachings of Karl Marx and other European socialist theorists and leaders, the secretariats eventually came to be viewed by the AFL-CIO leadership as a bulwark against efforts by communists to take over workers' organizations, particularly in developing nations.

More than 50 AFL-CIO affiliates, with nearly 60 percent of its total membership, are active in trade secretariats.

Kirkland--devotee of matters foreign, friend of diplomats and rulers, frequent traveler abroad--embodies labor's ancient international preoccupations.

Since he agreed to serve on the Reagan-appointed Central American commission headed by his friend, Kissinger, this bent has been magnified. Kirkland has spent the bulk of his time recently focusing on and traveling in Central America.

While much of the American public has only recently "discovered" El Salvador, the AFL-CIO has been at work there, as in many other places, for decades.

By all accounts, field workers for its American Institute for Free Labor Development (AIFLD) have been architects and builders of the Salvadoran land reform program. They work closely with Salvadoran peasants and trade-union leaders viewed as being in the center of the country's political spectrum, subject to attack from anti-reform guerrillas and right-wing death squads.

While labor might be expected to support the Reagan administration's policy of military and economic aid to the anti-communist rightist government in El Salvador, the AFL-CIO has edged further from the administration's position, particularly in the last few weeks, on grounds that trade-union interests are being pummeled.

In early 1981, two American AIFLD representatives and a Salvadoran land-reform leader were shot to death as they dined at a San Salvador hotel.

Labor leaders and other critics have charged that the administration and the Salvadoran government have resisted action on the case because of persuasive evidence that Salvadoran military officers committed the murders. The AFL-CIO has opposed military aid to El Salvador until the government brings them to justice.

The AFL-CIO recently broadened its opposition to include concern for Salvadoran land reform. Although the Reagan administration has supported the program as a key to democracy in the country, labor leaders say it is near collapse because of military-backed terrorism and murder and a recalcitrant government bureaucracy.

This change in the AFL-CIO's position has quelled much of the division in its ranks over the issue of involvement in El Salvador.

Still, some labor officials complain privately that Kirkland is too preoccupied with foreign affairs.

Also, a long-running conflict still exists between hard-liners led by Kirkland and more progressive union leaders. But it is softened, officials said, by Kirkland's open style and the fact that everyone is in accord on the foreign policy issue topping the hard-liners' priority list: trade and its effect on domestic jobs.

Don Stillman, political director of the United Auto Workers, said, "There's no doubt we are to the left of the AFL-CIO on foreign policy issues. But I don't think you have some of the communications difficulties that existed back in the Meany era. The old days of real arch-combat are long gone."