Cuban Americans, who make up 80 percent of the 750,000 Latins in the Miami region, have made this city a center of support for President Reagan's tough approach on Central America.

To an unusual degree, foreign policy is what counts in the politics of this Caribbean-oriented city, particularly toward Latin America. And Reagan's stand against President Fidel Castro and his allies has delighted the Cuban refugee families here.

The Spanish-accented cheers that greeted the president's speech here yesterday were undampened by complaints about the economy or fears expressed elsewhere about U.S. policy in Central America. And as a result, the city provided a backdrop for Reagan as a champion of Hispanics and a statesman blocking leftist challenges in the Caribbean and Latin America.

The presidential gesture of traveling to Miami, in the eyes of Cubans here, also represented acknowledgment of support the administration has received from Cuban Americans.

Unlike Hispanics in California and Texas, and almost exclusively for foreign policy considerations, the Cubans tend to vote Republican and conservative in national elections.

Dade County Republican Chairman Roberto Godoy, who is Cuban, said the county is the only one in the country with more registered Hispanic Republicans than Hispanic Democrats.

"This is a turning point for Cuban Americans," said Jorge Mas Canosa, chairman of the Cuban American Foundation, which hosted Reagan.

Mas Canosa, a Miami businessman, recently has been spending three days a week in Washington lobbying in Congress for administration plans to broadcast anti-Castro news to Cuba through a new facility, Radio Marti, that is strongly backed by Miami's anti-Castro Cubans.

"They've put a lot of store in President Reagan; they have a lot of faith in him," said Mary Collins, a state Republican Party committeewoman. "I think he reciprocates."

Cuban Americans in Dade County, which encompasses Miami, voted 86 percent for Reagan in 1980, compared with a 56 percent countywide edge for him. As a candidate Reagan received one of his warmest receptions during a visit to Miami's Little Havana neighborhood.

"He doesn't have to come down here to get the Cuban-American vote," Mas Canosa said. "He already has it."

About 2,000 Cuban, Nicaraguan and Salvadoran refugees rallied in a downtown park April 27 as Reagan addressed a joint session of Congress seeking support for his disputed Central American policies. Godoy said the demonstration was organized in part because of calls to Miami's Spanish-language radio stations from listeners who wanted to show support for Reagan.

Three days later, when an anti-administration group called a news conference at the same spot to denounce Reagan's speech, Cuban refugees broke it up, shouting "Viva Reagan." Within minutes, a man with a rifle fired a shot over their heads. Bystanders reported that the gunman thought those shouting were still the anti-Reagan demonstrators.

At another level, Mayor Maurice Ferre recently asked Diario Las Americas, a Spanish-language Miami newspaper, to publish his disavowal of a report issued by a prestigious commission on which he served under the chairmanship of Sol Linowitz, former U.S. ambassador to the Organization of American States, and Galo Plaza, former president of Ecuador.

The report, from the Inter-American Dialogue, called for emphasis on negotiations in Central America instead of the Reagan administration's emphasis on confronting leftist groups.

In a city whose mayor has such concerns, it perhaps is not unusual for Mas Canosa's group to make passage of Radio Marti legislation its major goal. The foundation lobbied strenuously last year for the original legislation, which died in a last-minute Senate filibuster after easy House passage.

For Mas Canosa, the administration is right in saying the United States should aim special broadcasts at Cuba as it does for the Soviet Union and eastern Europe with Radio Free Europe and Radio Liberty. The Voice of America, which already broadcasts to Cuba in Spanish, is barred by its charter from hostile propaganda.

Amended legislation is being considered by the House Foreign Affairs and the Senate Foreign Relations committees. Under its provisions, Radio Marti would broadcast at 1180 in AM frequencies from VOA facilities in Marathon, Fla., or from rented commercial facilities.

Despite the changes from last year's version, the legislation is still opposed by the National Association of Broadcasters. The group, representing U.S. radio stations, cites Cuban warnings that Havana will jam U.S. broadcasts to retaliate if Radio Marti goes on the air.

Cuban transmitters last Aug. 30 demonstrated their ability to do so, staging an evening of 250,000-watt disruptions that scrambled commercial signals as far as the Midwest.

Mas Canosa, reflecting the Cuban American sentiments that make Reagan a natural ally, said, "Basing our foreign policy on threats from a foreign dictator is not so intelligent. And that is what they want us to do."