Republican National Committee Chairman Richard Richards warned yesterday that organized labor "will find itself out of the mainstream of American politics" if it continues its increasingly cozy relationship with the Democratic Party.

"I believe it would be a grave error if we ever reach the point in American political life when members of organized labor conclude they are for one party only," Richards told delegates to the annual legislative conference of the AFL-CIO Building and Construction Trades Department.

"The end result will obviously be a determination by the Republican Party--if we cannot receive your support in any event--to quit trying.

"At the same time, equally or more damaging would be the fact that the Democrats would think that you belong to them and believe that you are in their hip pocket, and they will no longer feel the need to try.

"In that event," Richards said, "organized labor will find itself outside of the mainstream of American politics and this would be a tragedy of major proportions."

Many of the 4,000 delegates, leaders of construction unions that supported Ronald Reagan in 1980, booed Richards' comments. They also booed, shouted, and laughed during an address yesterday by Labor Secretary Raymond J. Donovan, who came to defend Reagan's economic program.

The president himself tried to regain support from the delegates in a speech to them on Monday. But he, too, drew some boos along with lukewarm applause.

Former vice president Walter F. Mondale and Sen. Edward M. Kennedy (D-Mass.), who spoke Tuesday, were welcomed as political heroes. The two potential rivals for the 1984 Democratic presidential nomination flayed Reagonomics and offered economic proposals--scuttling the administration's multiyear tax-cut strategy, pressuring the Federal Reserve Board into lowering interest rates, imposing credit controls and reinstituting public works programs--largely supported by the AFL-CIO leadership.

Richards said he "asked for the invitation" to speak to the delegates yesterday "to discuss building bridges between labor members and the Republican Party." He said the Republicans are forming a national labor advisory committee "comprised of labor representatives to advise the RNC on ways to develop a constructive dialogue with representatives of organized labor." He also said the RNC is placing a labor representative on its executive committee. He did not identify these labor representatives.

By comparison, 15 AFL-CIO members hold seats on the Democratic National Committee, and five others sit on the DNC's executive committee. Last February, in addition to union members on the committee, the DNC formed a 20-member Labor Council. The council, consisting of national and international union presidents, has as its first goal the election of a pro-labor Congress in November.

AFL-CIO President Lane Kirkland has often said he would like to have a similar relationship with the Republican Party. But he and other union leaders say the Reagan administration's alleged embrace of antilabor policies has shut the door to organized labor. The latest AFL-CIO complaint is with the administration's decision allowing hospitals to use Medicare funds to hire consultants who specialize in blocking union organizing--.

Richards said yesterday that the door is now open. "We want a dialogue. We want to talk. . . . We aren't talking about a brief relationship. We're talking about long range," he said.