The Supreme Court agreed yesterday to consider some of the most contentious social issues in America. The court ended a two-year hands-off policy on school busing cases by agreeing to decide whether voters can prevent state courts or local school boards from imposing busing plans.

It said it will consider the authority of school boards to remove what they consider objectionable books from school libraries and classrooms.

And it accepted for review the question of whether the government can revoke the tax-exempt status of religious schools that practice racial discrimination.

In the busing cases, the justices will consider the constitutionality of successful antibusing initiatives by voters in California and the State of Washington. Washington banned the busing of students without a court order. That measure, ultimately invalidated by lower federal courts, was designed to end busing in Seattle, Tacoma and Pasco required by school boards.

Californians amended their constitution to prohibit state courts from ordering busing except where there was proof of intentional school segregation. The amendment, ratified as "Proposition 1," ended extensive busing in Los Angeles ordered by state judges.

The busing cases, Washington vs. Seattle School Dist. No. 1 and Crawford vs. Board of Education of Los Angeles, do not directly involve the power of the federal courts, which have ordered most of the nation's busing. The question in both of yesterday's cases is whether citizens' votes to overturn the actions of state and local governing bodies discriminate against blacks.

If the answer is no, other states will undoubtedly fashion their own new restrictions, prompting more actions in federal courts.

But the authority of the federal courts in this arena is also jeopardized by congressional efforts to strip them of their power to order busing.

The Washington case attracted nationwide attention last month when the Justice Department, reversing the position taken by the Carter administration, argued that the Washington voters' initiative was not discriminatory. It did not interfere with any court order, the government said. It merely shifted the authority over pupil assignment from local school districts to the state, without regard to race.

On the other side, lawyers in both the California and Washington cases contend that these laws are specifically directed against the interests of blacks and minorities and are therefore unconstitutional.

The court's action yesterday suggests that at least some justices now believe that they can command a majority on the issue. For the past two years, following fragmented and confusing school desegregation rulings during the mid-1970s, the court has declined to rule on busing. The reason, many observers believe, was that the justices disagreed and they feared causing more confusion on such a sensitive issue.

The court also agreed to enter a nationwide controversy over books. School officials across the country are faced with demands, largely from conservative and fundamentalist organizations, to purge their libraries and curricula of books these groups consider objectionable.

A Long Island school board, the Island Trees Union Free School District, removed nine books under just such pressure. They included "The Fixer" by Bernard Malamud, "The Naked Ape" by Desmond Morris, "Soul on Ice" by Eldridge Cleaver and "Best Short Stories by Negro Writers," edited by Langston Hughes. The protesters objected to passages featuring colloquial or explicit sexual terms, disparagement of religion, and profanity.

Five students brought suit, charging that the action amounted to censorship forbidden under the First Amendment. School officials argued that their actions did not prohibit anyone from reading these books, they just made them inaccessible in the schools. Therefore, they argued, the federal courts have no business hearing the students' complaint, removal of the books was solely a matter of local school board discretion.

The Second U.S. Circuit Court of Appeals disagreed, however, ruling that the school board officials' haphazard review of the materials suggested that they were trying to establish their own views "as the correct and orthodox ones for all purposes in the particular community." That, the appeals court said, might be unconstitutional censorship. It allowed the students to proceed to trial.

The school board appealed to the justices, asking them to rule that there is no censorship issue in the case and therefore no reason for a trial.

Another school case may resolve a 10-year-old controversy over the use of the tax laws to discourage racial discrimination. In 1970, the Internal Revenue Service started moving against discriminatory private schools by revoking or denying the tax-exempt status given nonprofit educational institutions.

One school that lost the lucrative benefit was Bob Jones University in Greenville, S.C. Bob Jones originally excluded blacks entirely but later changed its rules to deal with what it said was its primary religious purpose, to prevent interracial marriage. It then excluded unmarried blacks and anyone known to be a partner in interracial marriage or affiliated with any group advocating interracial marriage or dating.

In another instance, Goldsboro Christian Schools in North Carolina were denied a tax exemption because of allegedly racially discriminatory admissions policies.

Both the university and the Goldsboro Christian elementary and secondary schools and numerous religious organizations are arguing that the actions of the government violate their religious rights. Both institutions have lost their cases in the lower courts.

Though disagreeing with them, the government asked the court to take the cases. Questions about constitutionality and the organized resistance of hundreds of schools around the country have "impeded" IRS enforcement, the government said.

In other action yesterday, the court agreed to review a search and seizure ruling that struck down a heroin conviction. Albert Ross, the defendant, was convicted in 1978 of heroin possession and sentenced to 20 years. But the U.S. Circuit Court of Appeals reversed the conviction because it was based on a warrantless police search of a brown paper bag in a car trunk.

In a Supreme Court opinion last year, the justices attempted to straighten out a long-running controversy about searches of articles in cars. That ruling appeared to conform with the appeals court ruling in the Ross case. But yesterday, in an unusual move, the justices asked the lawyers to address the question of whether last year's decision should be reconsidered.