Only a few days after President Carter told federal workers that none would have their careers disrupted by government reorganization, the Navy Department decided recently to abolish an installation here and transfer, demote or fire 77 of its civiliam employees.

The Washington area's six members in the House of Representatives protested the closing of the unit - the Naval Electronic Systems Engineering Center - in a joint letter sent yesterday to the Pentagon and the White House.

Of the 109 employees, an estimated 59 would be transferred to Portsmouth, Va., nine would be transferred to Charleston, S.C., and nine others - workers in a machine shop would be fired as a result of what the government calls "reduction in force," or RIF. Another 32 workers would be transferred to another Washington office.

The decision to shut the center, which occupies an industrial-type building at the historic Navy yard in Southeast Washington, was made late last month by Navy Secretary W. Graham Claytor Jr., a Carter appointee and former board chairman of the Southern Railway System.

It was annouced in a directive signed Feb. 22 by Rear Adm. E. B. Fowler, commander of the Naval Electronic Systems Command. Although the action takes effect March 31, the actual shift of personnel would not be completed until June 30.

The letter, drafted by Rep. Gladys N. Spellman (D-Md.), did not seek an outright reversal of the move, but asked Claytor to defer the shift "until your office has reviewed this situation to make it consistent with the avowed policies of the new administration."

Last year, Mrs. Spellman fought unsuccessfully to block the Ford administration's move of 1,300 Naval Oceanographic Office employees from Suitland to Bay St. Louis, Miss.

On the impending closure issue, Mrs. Spellman cited statements the President made to government workers in a round of visits to several departments last mont.

At the Commerce Department on Feb. 9, for example, he said: ". . . Changes in the structure of government will not adversely affect your own careers under any circumstances. If it ever does, you contact me directly . . ."

A Navy Department spokesman, asked how the action squared with the President's statements, said the Navy "is not in receipt of any directive that prohibits reductions in force." He said the closure had been under consideration since last June.

The "Disestablishment" of the unit which has the Navy code name NAVELEXSYSENGCEN, was "made necessary because of continuing reductions in civilian (employment) ceiling available . . . to carry out mission responsibilities," Fowler wrote. He said many alternatives to the closure were considered during the long period prior to Claytor's final decision.

In the letter sent to Claytor, with copies to the President and to Defense Secretary Harold Brown, the members of the Metropolitan Washington caucus in the House said the closure was "initiated in a fashion which adds to out apprehension in behalf of the employees.

"The employees received notive of this relocation and RIF only in the past week; yet they must indicate their intentions by March 31, 1977," the letter asserted.

"Those who will be subject to a RIF have, of course, been given no other options. those who might be subject to downgradings (demotions) have not been fully informed, as of this date."

The letter noted that many of the workers are middle'aged persons who have lived in or around Washington most of their working lives.

In addition to Mrs. Spellman, the letter was signed by Reps. Joseph L. Fisher (D-Va.), Herbert E. Harris (D-Va.), Newton I. Steers (R.Md.) and Marjorie S. Holt (R-Md.) and Del. Walter E. Fauntroy (D-D.C.), the caucus chairman.

On another matter, the caucus agreed to meet with Federal Aviation Administration officials to insist upon creating an effective shuttle bus system to carry people between the National Airport terminals and the Metro station when train service starts there July 1.