Leaders of organized labor in Washington will celebrate the traditional Labor Day Mass at Sacred Heart Church today, but afterward much of the worker solidarity the ceremony is supposed to symbolize will stop at the church's door.

After the morning service at 16th Street and Park Road NW, labor leaders and rank-and-file workers, their house divided, will split into opposing political camps.

The backers of Mayor Marion Barry will head for a picnic of beer and hot dogs at Kenilworth Park off Anacostia Avenue in Northeast Washington, while supporters of his chief rival, Patricia Roberts Harris, attend a private cookout in Chevy Chase.

And for the second time in four years, organized labor in Washington finds itself on the eve of a Democratic mayoral primary with its local political clout in doubt.

In 1978, the unions were nearly unanimous in their effort to reelect former mayor Walter E. Washington, with only a few public-sector unions splitting off to support underdog Barry and the Teamsters going their own way with Sterling Tucker. Despite that support, Washington lost. And the value of labor's support to D.C. candidates has been sharply debated since.

This year, Barry, whose administration signed contracts considered favorable with the unions representing city workers, is getting the support of most of those public-sector unions -- despite severe budget cuts and layoffs a few years ago that had those same union members marching in the streets against him.

Harris has picked up the endorsement of most of the private-sector unions, including the building trades and hotel and restaurant workers.

The split has left local labor's umbrella organization, the Metropolitan Washington Council, AFL-CIO, on the political sidelines in the city's biggest race, and guarantees that about half of organized labor will be on the outs with whichever candidate wins.

"The council is neutral," said council president Joslyn (Josh) Williams. The council, formerly named the Central Labor Council, represents about 150 unions with 225,000 members in the metropolitan area.

Williams said the only bright spot this year is the unified support for Ward 1 City Council member David A. Clarke, who is running for chairman of the City Council in the Sept. 14 primary. Clarke has captured all the union endorsements except for the Washington Teachers Union, which has endorsed incumbent Arrington Dixon.

"The true test is whether labor can make a difference in the chairman's race," Williams said recently. He said labor supported Clarke, who is in a tight race with Dixon and former chairman Sterling Tucker, when Clarke was given little chance to win.

"I'm not saying the candidate must in fact win," Williams said, " . . . but how well he performs on election day will say quite a bit about what labor can and can't do in this city."

Some of the private-sector unions have stopped paying dues to the labor council, preferring instead to spend the money in this year's campaigns, a move that Williams said has only hurt the council's ability to keep the unions together on other issues.

Ron Richardson, executive secretary of the Hotel and Restaurant Employees Local 25 and a leader of the pro-Harris faction, contends the mayoral split has only aggravated a longstanding dispute within the labor council between the public-sector and private-sector unions. Each makes up about half of the umbrella organization.

"This has been going on a long time," he said, rejecting charges that he is supporting Harris to spite the public unions.

Richardson criticizes the Barry administration for cutting workers' compensation and unemployment benefits, in addition to sharply criticizing the mayor for the D.C. government employe layoffs of two years ago. He contends the public-sector unions are supporting Barry now only because of "sweetheart contracts" Barry signed earlier this year.

"It was masterful. He whacked the hell out of them with a stick, and when they were bleeding, he reached out and handed them a carrot," Richardson said. "We're in favor of people getting . . . benefits, but it is one thing to negotiate them and another to swap support for it, especially for someone who has taken a swath out of your membership."

Bernard Demczuk, a former jail guard who helped organize a wildcat strike for better working conditions in 1979 and led public demonstrations against Barry's budget cutbacks, supports Barry now and disagrees with Richardson.

"It's different times now," said Demczuk, who works as a $29,000-a-year organizer for the American Federation of Government Employees. "Barry has been much more supportive of public unions. The name of the game in politics for public service employes is we have a chance to elect our boss. The stronger we are politically in this city, the stronger we are at the negotiating table."