The Supreme Court yesterday repudiated the Reagan administration arguments and ruled unequivocally that the government can and should withold tax benefits from private schools that violate "a fundamental national public policy" by practicing racial discrimination.

The court, in an 8-to-1 decision written by Chief Justice Warren. E. Burger, rejected the administration's position that the Internal Revenue Service lacked legal authority to deny charitable tax exemptions to the two schools involved in yesterday's case, Bob Jones University and Goldsboro Christian Schools.

The IRS has the authority to deny exemptions to any institution acting "contrary to established public policy," the court said. "There can no longer be any doubt that racial discrimination in education violates deeply and widely accepted views of elementary justice," Burger wrote.

The court also rejected the schools' claim that the IRS, by denying them tax exemptions, has unconstitutionally inhibited their religious practices -- which they say require racial discrimination. The governmental need to eradicate discrimination in education "substantially outweighs whatever burden" the policy places on the schools' religious beliefs, the court said.

Only the court's most conservative member, Justice William H. Rehnquist, dissented from yesterday's decision, Justice Lewis F. Powell Jr. wrote a separate concurring statement.

The decision climaxed what many consider the administration's most damaging civil rights confrontation. The IRS had been denying the exemptions to discriminatory private schools since 1970 as a way of discouraging the growth of "segregation academies."

The schools had attacked the IRS policy before the Supreme Court and the government was fighting the schools' arguments. But in January, 1982, the Reagan administration revoked the IRS' authority to deny tax exemptions, saying it required explicit congressional authorization.

Then the Justice Department switched sides before the Supreme Court and attempted to head off a ruling. Instead, the court appointed William T. Coleman Jr., a prominent black lawyer and former secretary of transportation, to replace the government in the cases.

Despite efforts to minimize publicity about the abrupt policy change and later attempts to soften it, the action raised a storm of protest, including a letter signed by 200 officials of the Justice Department's Civil Rights Division, and came to symbolize the new president's sharp break with civil rights policies of the past. It opened a breach in his relations with civil rights leaders that has only widened since.

Yesterday's decision means the IRS can continue its practice without an act of Congress. That spares Congress from an unpleasant and sensitive task. At the same time, it will cost millions of dollars for more than a hundred schools that discriminate against blacks. Tax exemptions free charitable institutions from all federal tax liability and encourage private contributions by making the donations tax deductible.

The IRS said Goldsboro owed $160,000 in unpaid taxes for the years 1969 through 1972 because of the denial, while Bob Jones University owed $489,000 for the years 1971 through 1975.

Bob Jones University, in Greenville, S.C., enrolls about 5,000 students at the college level. Bob Jones argued before the Supreme Court that its religious beliefs require separation of the races. The school originally denied admission to all blacks. In 1975, however, it modified its admissions regulations to allow black students but continued a ban on interracial dating and marriage.

Goldsboro Christian Schools, of Goldsboro, N.C., has maintained a racially discriminatory admissions policy since it was founded in 1963. It also cites the Bible for justification. The schools challenged the IRS denial of tax exemptions in the Supreme Court after unsuccessful efforts in the 4th U.S. Circuit Court of Appeals.

Congress first enacted a provision exempting charities from taxation in 1894, the court said yesterday. "Charities were to be given preferential treatment because they provide a benefit to society," Burger wrote. They must "demonstrably serve and be in harmony with the public interest."

He said that since Brown vs. Board of Education, the 1954 Supreme Court decision declaring racially separate school systems unconstitutional, discrimination in the schools has clearly been against the public interest. Laws passed by Congress and presidential actions against school discrimination over the past 30 years have buttressed that determination, the chief justice said.

The IRS properly responded in 1970 by issuing the regulations denying tax exemptions to discriminatory schools, Burger said. The action was "wholly consistent with what Congress, the executive and the courts had repeatedly declared . . . . Indeed, it would be anomalous for the executive, legislative and judicial branches to reach conclusions that add up to a firm public policy on racial discrimination and at the same time have the IRS blissfully ignore what all three branches of the federal government had declared."

Since then, he said Congress has endorsed the practice implicitly by refusing on 13 different occasions to pass bills barring the IRS policy.

Powell, in his concurring statement in Bob Jones University vs. U.S., agreed that exemptions may be denied to further the "fundamental" public policy against school discrimination. But he said the majority ruling gave the IRS too much authority to determine whether other institutions violate other public policies.

The majority suggests that "the primary function of a tax-exempt organization is to act on behalf of the government in carrying out governmentally approved policies," Powell said. "The contours of public policy should be determined by Congress, not by judges or the IRS," he said. Rehnquist, the lone dissenter, said that only Congress -- not the IRS -- was empowered to define the requirements for tax-exempt status. "Regardless of our view on the propriety of Congress' failure to legislate," he said, "we are not constitutionally empowered to act for them."