A Republican-backed plan to redistrict Fairfax County this year collapsed yesterday when County Attorney David T. Stitt declared as constitutional a bill passed last month by the Virginia General Assembly that prevents the county from redrawing its eight supervisory districts until after the 1990 census.

Fairfax Republican supervisors, who hold a 5-to-4 majority on the county board, had said they intended to redistrict the county despite the bill passed by the Democraticcontrolled state legislature.

But Stitt's 13-page memorandum, presented to the board in executive session yesterday and then released to the public, concludes that the bill violates neither the equal protection clause of the U.S. Constitution nor provisions of the Virginia constitution.

Republicans on the county board immediately abandoned their plan to redistrict the county, which was to have proceeded today with the authorization of public hearings.

"It confirms what we have said for several weeks now," said Supervisor James M. Scott (D-Providence): "That redistricting as the Republicans proposed to do it is illegal."

"The opinion by Stitt is clear and unequivocal," said County Board Chairman John F. Herrity, a Republican who had accused Democrats in the state legislature of "shabby, Chicago-style politics" and promised that "we are not going to let them get away with it."

Democrats on the county board said that when Stitt presented his memorandum in executive session, Herrity was angered and said he would seek another opinion.

Speaking to reporters after the memorandum was made public, Herrity acknowledged that he had reacted angrily at first. "No, I don't agree with it," he said. "But I accept reality."

Thomas M. Davis III (R-Mason) said the Republicans' decision to give up the redistricting plan this year was "the responsible thing to do."

Democrats said, however, that Stitt's memorandum left the Republicans little choice. To persist with redistricting despite the memorandum, members of both parties said, would have led to an expensive legal battle with little prospect of Republican success.

Republicans had argued that sharp disparities in population growth around the county warranted redrawing political boundaries. For example, the fast-growing Springfield District in western Fairfax has more than 100,000 people, while Lee District, a more established area in eastern Fairfax, has just 70,000. The disparities, Republicans said, violated the principle of one man, one vote.

Democrats contended that redistricting is disruptive and unnecessary, and they charged that the Republicans' primary motivation in redistricting was to unseat Scott, a liberal who has won election narrowly. Republicans denied that Scott was a target.

The supervisors, who serve four-year terms, are up for reelection in November 1987.

Republicans hinted they may try again next year to redistrict the county. Under state law, they said, they are free to redraw the boundaries in an election year if they also change the number of supervisory districts.

In a motion offered by Herrity and backed by his four Republican allies on the board, the supervisors voted to consider next year redistricting the county to comprise seven, nine or 10 districts.

Stitt's memorandum was reviewed by A.E. Dick Howard, dean of the law school at the University of Virginia, who agreed with its conclusions. Howard was executive director of the commission that wrote Virginia's new constitution in 1971.

In an interview yesterday, Howard said that although the U.S. Supreme Court has upheld decennial reapportionment under the equal protection clause of the 14th Amendment, the court has never gone beyond that to require more frequent redistricting.

He also said the General Assembly was within its rights in forbidding Fairfax to redistrict this year.