The Internal Revenue Service ran into a barrage of opposition yesterday on proposed new rules to revoke the tax exemptions of private schools that discriminate against minority students, all but guaranteeing that the agency will have to give ground.

Although IRS officials made no formal concessions on the issue, protests at the start of a four-day hearing were so strident that all sides agreed privately the agency would have to compromise to avert a fight with Congress.

The IRS now is expected to propose revised, less-stringent rules, possibly after a House Ways and Means oversight subcommittee holds hearings on the issue, now set for mid-January. Insiders say the only question is how much the IRS will have to cut back.

Yesterday's protests came during an emotionally charged hearing at which opponents attacked the IRS rules as arbitrary, unconstitutional, overly restrictive and a usurpation of Congress' legislative role -- often to heavy applause from spectators.

At one point, June Griffin, a member of the audience, rose out of turn to denounce the IRS hearing officers for prying into the lives of citizens. "These men do not have the right," she shouted, "to tell us how to run our schools, our homes, our churches!"

The dispute stems from efforts by the IRS to beef up its ability to enforce the laws requiring it to revoke the tax exemption of "segregation academies" -- private schools set up as havens to which white pupils can flee when regular public schools are ordered to desegregate.

Under current rules, the IRS must continue granting these schools tax-exempt status as long as they publicly disavow discriminatory practices -- even if a court has ruled that theschool is in violation of the 1964 Civil Rights Act. Many retain their exemptions today

The IRS tried to eliminate this disparity last August by proposing a two-part "test" to decide whether a private school has been discriminating. However, thousands of legitimate private schools -- including many church-related groups -- have complained they would be hurt as well.

Yesterday's opposition included 15 members of Congress, dozens of private school officials and one former IRS commissioner, Randolph W. Thrower, a Nixon administration appointee who is a private tax lawyer in Atlanta.

In all, almost 250 persons are scheduled to testify between now and late Friday, when the hearings are slated to end. Moreover, officials say they have received an estimated 100,000 letters -- the bulk of them opposed to the new regulations.

Particularly upset are officials from suburban schools and from schools sponsored by religious groups unlikely to have many blacks as members -- such as Amish or Hebrew schools. Protesters said requiring these schools to meet racial requirements would be unrealistic.

William J. McMillan, president of the Florida Association of Academic Non-Public Schools, pleaded that "there simply is not a large-enough proportion of blacks among Jewish students in Southeast Florida" to meet the proposed IRS guidelines.

And Sen. Strom Thurmond (R-S.C.), who appeared as a witness yesterday, argued that the IRS proposals would mark "a radical departure from traditional concepts," and would force some private schools to close. He urged the IRS to allow Congress to write new guidelines.

Thurmond, once an avid foe of school desegregation efforts, insisted his protest was not intended to thwart the fight to eliminate discrimination in schools. "It is impossible," he declared, "for a reasonable man to argue against that."

The new IRS proposals would apply only to two categories of private schools -- those under formal court order to desegregate, and those that were established or expanded sharply after public schools in their locality were desegregated.

The proposals would establish "tests" for IRS officials to use in deciding whether a private school is discriminating. The school either would have to enroll a minimum number of minority pupils, or else show it is moving actively to recruit them.

The minimum would amount to 20 percent of the total proportion of minority students in a community. So, if minorities comprised 30 percent of a locality, the school would have to have an enrollment that is 6 percent minority to qualify.

If a school could not meet that test, the new IRS rules would require that it fulfill four of five other requirements, from conducting a minority recruitment program to providing special scholarships and employing more minority teachers.

Denial of a tax exemption is a major financial setback for most private schools. Not only do they lose tax-free status for their own income, but persons contributing to the school no longer are allowed to take deductions for their donations.

The IRS proposals were supported unequivocally by the Departments of Justice and of Health, Education and Welfare and by a handful of civil rights groups and civic organizations.James P. Turner, deputy assistant attorney general for civil rights, called them fair and badly needed.

Clarence Mitchell, former Washington lobbyist for the NAACP, chided church officials for opposing the regulations. "Every school that's been started to evade desegregation has called itself Christian," he said. "That's not my idea of being Christian."