The Supreme Court, with the Reagan administration's tuition tax credit proposal looming in the background, yesterday heard Minnesota attorneys argue the constitutionality of allowing state financial aid to parents of parochial school students.

Minnesota law allows parents of private and public school students to deduct from their state income taxes the costs of school tuition and fees.

It was the 19th time in 35 years that the court has heard such pleas. The justices have usually rejected them, on the grounds that the aid plans are unconstitutional subsidies of religion.

But yesterday, during an hour of oral argument at the court, Minnesota Assistant Attorney General Douglas C. Blomgren argued that this law was different from the others because it is an indirect form of aid that benefits both private and public school parents and is thus "neutral" and "secular" in its purpose.

William I. Kampf, the lawyer for those challenging the law, argued that the inclusion of public school parents under the law was simply a cover for a program in which the vast majority of beneficiaries are the parents of parochial school students. Public school students almost never pay tuition, he noted, while virtually all private school enrollees must pay.

The aid plan "subsidizes an activity intended to inculcate religion," Kampf said. "Just as states may not provide direct aid to religion , they may not provide indirect aid, through deductions, tax credits or anything else."

Despite the number of Supreme Court decisions over the years, lower courts continue to divide on the church-and-state issue. A Rhode Island program similar to Minnesota's was recently struck down by the 1st U.S. Circuit Court of Appeals while the 8th U.S. Circuit Court of Appeals upheld the Minnesota law, resulting in the argument in Mueller vs. Allen yesterday.

Blomgren told the justices that the law was no more unconstitutional than the almost universal property tax exemptions allowed for church property or the federal tax deductions allowed for charitable contributions to religious organizations. It does not "provide the active sort of assistance that constitutes state sponsorship," Blomgren said.

Someone could donate buses, books and "even Bibles" to a church school, he said, and deduct the value from his federal income taxes. "But if a person with a child in a parochial school takes a deduction, that's going to be considered unconstitutional? It is impossible to reconcile" the two situations, he said.

Under the program, parents may deduct up to $500 for the costs of educating children in kindergarten through sixth grade and up to $700 for the costs of children in the remaining grades.

The total deductions taken in 1978 under the program for public school students was $5.2 million. For non-public school students, the total was $14 million.

Kampf said such figures demonstrate the primary beneficiaries of the law. It is different from deductions for charity, he said, because it offsets the cost of a service directly received by the parents. "It is a quid pro quo, an exact dollar for dollar service, like medical deductions or home interest deductions."

It is different from property tax exemptions for churches because that benefit is "historically embedded" to protect religion from taxation, Kampf said.

The Minnesota case has attracted a massive outpouring of friend-of-the-court briefs. The Reagan administration, hoping to get Congress to enact its own tuition tax credit plan, has come in on the side of Minnesota. So have the United States Catholic Conference, the Mountain States Legal Foundation, and others.

Kampf is being supported by the American Civil Liberties Union, the National School Boards Association, Americans United for Separation of Church and State, the Baptist Joint Committee on Public Affairs, the American Jewish Congress, the AFL-CIO and the National Parent Teacher Association, among others.