The Supreme Court agreed yesterday to consider whether the NAACP can be held financially responsible for the economic losses of businesses it targeted in Mississippi for a highly publicized 1966 civil rights boycott.

The court also will review the power of courts to block such boycotts, which the NAACP says are protected by constitutional free-speech guarantees.

The case (NAACP vs. Claiborne Hardware Co.) attracted national attention when a Mississippi court ordered the NAACP to pay $1.25 million to the merchants of Port Gibson, the boycott targets, which threatened the country's most famous civil rights organization with bankruptcy. The state's Supreme Court later said that amount was excessive and ordered it reconsidered. The dollar amount is not the issue before the high court justices.

The three-year boycott began as a way of dramatizing what the civil rights leaders considered a pattern of blatant discrimination in Claiborne County, Miss. They said that county schools, the county courthouse, the county hospital and public facilities in general were still segregated and that blacks were discriminated against in public and private employment.

The boycott of white-owned businesses featured demonstrations, picketing and leaflet distribution. The merchants said it also involved threats and violence (a charge denied by the boycott organizers), and successfully sued to end the action and recover their business losses.

The Mississippi Supreme Court ruled that the activists lost their free-speech protection when the boycott got violent. It became a conspiracy, the court said, unprotected by the First Amendment.

In other action yesterday:

* The court entered a dispute between the State Department and The Washington Post over the Freedom of Information Act and what information can be withheld as too private for public consumption.

During the 1979 U.S.-Iranian crisis, The Post asked the State Department whether two Ayatollah Ruhollah Khomeini regime officials, Ibrahim Yazdi and Ali Behzadnia, were naturalized American citizens carrying U.S. passports, as had been reported in the press but denied by Yazdi.

The department refused to provide the relevant data, saying it could jeopardize and maybe lead to the death of the two officials. The information act's exemption for information invading personal privacy was cited as grounds for withholding the data.

The Post successfully challenged the denial in court, saying that naturalization records are routinely a matter of public record. The Court of Appeals for the District of Columbia ruled in favor of The Post. The "privacy" exemption, it ruled, covers only "intimate" details about someone.

In its appeal to the Supreme Court, the State Department said that ruling has potentially "far-reaching consequences in view of the vast store of personal data about individuals" contained in government files. The government should be able to withhold information on the grounds that its release could harm someone, the government said, adding that is "the most palpable example of an invasion of personal privacy."

* The court agreed to hear the Ford Motor Co.'s contention that it was unfairly judged guilty of sex discrimination at its Charlotte, N.C., auto parts warehouse and subjected to a back-pay award.

Ten women brought their complaint to the Equal Employment Opportunity Commission after men were hired for jobs the women had unsuccessfully sought.

Ford contends that the lower federal courts applied an improper standard in the case (Ford Motor Co. vs. EEOC), making the company responsible if it could not prove a legitimate, nondiscriminatory reason for its employment decisions. It also disputes the method by which the back pay was calculated.

* The court (in Caffiero vs. Board of Education of Piscataway) left untouched a New Jersey law, similar to those in more than 40 other states, making parents financially responsible for the vandalism of their children.

* The justices upheld a U.S. Court of Appeals ruling striking down the state of Washington's obscenity law before it was enforced. The lower court held the law unconstitutional in part because it allowed officials to ban sale or exhibition of films that had not been declared legally obscene. That affirmance (Donald C. Brockett vs. Spokane Arcades) came over the objections of Chief Justice Warren E. Burger and Justices Lewis F. Powell and William H. Rehnquist. They said in a dissent that the federal courts had no power to intervene in Washington's affairs before state courts had even considered the law or any specific charges brought under it.