The Fairfax County School Board complied last night with the county supervisors' demands to slice $4.3 million from the school budget, making almost half the required reductions in ways that will not require cuts in programs and operations.

The cutback represents about 1 percent of the school system's $425 million budget for the 1982-83 school year.

The most controversial cut was the elimination of $370,000 for a dental and vision insurance package for school employes. The board approved the insurance contribution last fall during discussions with the county's teacher organizations.

"This is an abrogation of the discussion process," said Marilyn Rogers, president of the Fairfax Education Association. "Now I'm very concerned about the process in the future."

Rogers said teachers agreed to accept a 5 percent cost-of-living raise based on the promise of employer contributions to the insurance.

The County Board of Supervisors made its $4.3 million cut from the school board's proposed $429 million budget last month, forcing school officials to begin a second round of budget debates.

School Superintendent Linton Deck originally recommended cuts to 23 programs, but doubled the list of proposed cutbacks when the board demanded more choices. Despite hours of agonizing, 4l percent of the reductions were made through such means as correcting overestimates, transfering funds between accounts and recognizing unexpected savings.

For example, the school staff had overestimated by $294,000 the inflationary increases in elementary school textbook materials.

Other cuts included elimination of 50 staff positions, many of them new jobs created in the board's original budget.

The board also made about three dozen relatively small cuts in a variety of programs.

In other action, the board, which sets the school calendar two years in advance, voted against observing the birthday of the Rev. Dr. Martin Luther King Jr. as a school holiday in 1984. The board has already decided not to observe a holiday next year, when the birthday, Jan. 15, falls on a Saturday. In 1984 the 15th falls on a Sunday, and board members said they did not wish to give up a school day to mark an anniversary that falls on a weekend. The schools observed the day as a holiday this year when it fell on a Friday.