A report yesterday on federal aid to parochial schools said the Supreme Court in the past had ruled such aid impermissible. In 1975, the court ruled only that a state aid program, not a federal program, was unconstitutional.

The Supreme Court, adding to a series of cases on its docket this term involving religion and government, agreed yesterday to decide whether federal funds can be used to send public school teachers to conduct secular classes in parochial schools.

The court already has agreed to hear a similar case from Grand Rapids, Mich., involving use of state funds.

The justices yesterday accepted the Justice Department's suggestion to decide whether the Constitution forbids using federal funds from the $3 billion Title I remedial education program to assist religious schools.

The 19-year-old program is the largest form of federal assistance to elementary and secondary schools.

Parents in New York City, joined by the city and the federal government, are asking the high court to overturn an appeals court ruling July 9 that said the program was an unconstitutional entanglement of government and religion.

About 13 percent of the $147 million New York City received in 1982 from the program went to assist religious schools, with more than 90 percent of the money going to Catholic or Jewish schools.

The court has in the past ruled that major programs of federal aid to parochial schools are impermissible.

The appeals court, in declaring the New York program unconstitutional, cited a 1975 Supreme Court decision involving a similar aid program in Pennsylvania. The cases are: Aguilar v. Felton; U.S. v. Felton, and New York City v. Felton.

The court also agreed yesterday to hear a case involving a section of the Alabama constitution that bars voting by people convicted of minor offenses "involving moral turpitude."

The 11th U.S. Circuit Court of Appeals in Atlanta ruled in April that the intent and effect of the 1901 provision were to limit the political power of black voters by using convictions for undefined petty offenses as a bar to voting.

Alabama officials argue that the state has a legitimate interest in barring voting by people convicted of crimes involving "moral turpitude," such as passing bad checks, and that the constitutional provision was not passed merely to exclude blacks. The case is Hunter v. Underwood.

Thirteen death row inmates failed yesterday to have the high court accept their appeals, but the justices granted one appeal from Mississippi murderer Bobby Caldwell, who argued that he was unconstitutionally denied state funds to hire fingerprint and ballistics experts to help his defense.

In other cases yesterday, the court: Declined to hear an appeal by a group of Americans held hostage in Iran who were attempting to sue the government of Iran for damages. Agreed to hear three Indian cases. One case, Oregon Dept. of Fish & Wildlife v. Klamath Indian Tribe, involves state powers to regulate fishing and hunting by Indians. A second case, Kerr-McGee Corporation v. Navajo Tribe, concerns taxes of oil and gas companies on Indian reservations, and a third case, Mountain States Telephone and Telegraph Co. v. Pueblo of Santa Ana, involves a dispute over the telephone company's right of way through a reservation. Agreed to decide whether state courts have the power to resolve nationwide class-action suits against out-of-state companies when most of the class members do not reside in the state. The case is Phillips Petroleum Co. v. Shutts. Agreed to decide whether New Mexico's residency requirement for veterans' tax benefits is constitutional. The case is Hooper v. Bernalillo County Assessor.

Court police yesterday removed a California man opposed to abortion from the back of the high court chamber after he shouted, "Thou shalt not kill" at the justices.

Steven Rediger, 31, of Stockton, stood up during a short break between oral arguments in cases involving patents and trademark infringement and, according to one witness, said: "Mr. Chief Justice and this honorable court. The law of God is that thou shalt not kill."

Rediger was questioned by court police and released. A court spokesman said no charges would be brought against Rediger. Such incidents occur at most once or twice a year, the spokesman said.