Grass-roots leaders of the government's biggest union exhibited symptoms of a split personality in their convention here this week:

The 1,600 delegates to the American Federation of Government Employees session breathed fire and booed at the mention of their big boss, Ronald Reagan, or any other Republican politician.

The union, which has 225,000 members and bargaining rights for 700,000 U.S. civil servants, reelected Ken Blaylock, who pledged to court congressional Democrats and work to defeat Republicans who have backed Reagan proposals to cap federal pay, defer pension increases and impose a Medicare tax on government employes.

But after endorsing Blaylock's call for government employes to play political hardball with the White House, the delegates here rejected a desperate plea from the union's leadership to vote a dues increase that would have cost members $6 a year to help finance the campaign to beat Republicans this fall and put a Democrat in the White House in 1984.

Late Friday afternoon, after many delegates had already checked out of their hotel rooms and stashed luggage in storage, the convention debated, and rejected, a variety of proposals ranging from a dues increase of 50 cents next year to a nickel-a-month increase in 1983.

The final vote on the resolution for a dues increase was 87,111 in favor, 62,711 against. Because any such constitutional change requires a two-thirds vote, the measure lost, a motion was made to adjourn and Blaylock, weary but resigned, conducted the let's-go-home vote and thanked delegates for coming.

Rep. Steny Hoyer (D-Md.) addressed the convention, telling how much federal workers have suffered at the hands of the administration. He also brought the bad -- but not surprising -- news that the president had formally recommended a 4 percent October pay raise for federal white-collar workers.

A government study had shown that federal workers were due an 18 percent pay raise to keep pace with the private sector. In rejecting a full catch-up raise, Reagan followed in the footsteps of the last three presidents.

After Hoyer spoke, Blaylock noted that there had been a lot of media attention to the pro-Democratic, anti-Republican course he plans to steer for the AFGE.

Blaylock said his strategy doesn't mean that the Democrats are going to "own" AFGE. What it means, he said, is that "after the November elections you [Democrats] are going to owe us . . . you are going to owe us full collective bargaining over pay . . . and the agency shop." Both of those IOUs that Blaylock hopes to collect with a Democratic-dominated Congress would require major changes in federal law and personnel practices.

Currently, federal unions are limited in what they can bargain for on behalf of members. They cannot bargain over pay, the length of the work week, fringe benefits or other issues that are the main reason people outside of government join unions. Nor can federal employes be required to join a union (the union shop) or be required to pay dues to unions representing them (the agency shop) if they do not want to join unions.

Past AFGE conventions have denounced the occupant of the White House of the moment -- Johnson, Nixon, and Carter. But leaders here said they had never seen a convention so unanimous in its hatred of the president.

"A third of our delegates are young employes with very little seniority or experience in government," a New England union leader observed. "They came into government because they thought it was a good place to work. Then they get hit with rifs and furloughs, which jolted the hell out of the old-timers too. They think they've been picked on by Reagan and treated badly. They are scared, and mad as hell."