The Supreme Court's ruling Tuesday guaranteeing a free public education to the children of illegal aliens is just the sort of opinion that conservative court critics cite when calling for legislation to strip the courts of jurisdiction over sensitive social issues.

In fact, few recent court decisions have so dramatically illustrated the long-running debate, now before Congress as it considers these court-stripping bills, over the role of the federal courts in American government. How often and under what circumstances should the judiciary overturn policy decisions made by elected government officials? And just how far can the Constitution be stretched?

In Plyler vs. Doe, Justice William J. Brennan Jr. declared that the Supreme Court would not tolerate the creation of an "underclass" in American society, one permanently oppressed by the denial of a free public education.

So saying, the 5-to-4 court overrode the legislature, school boards and governor of Texas, struck down laws requiring tuition payments from illegal aliens and extended the Constitution to places it had never been before. Now, for the first time, it guarantees equal treatment to people who have no legal right to be in the United States.

Plyler vs. Doe was a challenge on behalf of Mexican school children to a Texas law excluding them from the free public schools. Both sides at the Supreme Court condemned the exclusion.

"It is senseless for an enlightened society to deprive any children--including illegal aliens--of an elementary education," Chief Justice Warren E. Burger wrote, with fellow dissenters Justices Byron R. White, William H. Rehnquist and Sandra Day O'Connor. "I fully agree that it would be folly--and wrong--to tolerate creation of a segment of society made up of illiterate persons," he continued.

But the agreement ended there because Burger and his allies, on the one hand, and Brennan have a profoundly different attitude about how the court should react when confronted with "senseless" social policy.

" . . . It is not the function of the judiciary to provide 'effective leadership' simply because the political branches of government fail to do so," Burger wrote in his dissent.

"The Constitution does not provide a cure for every social ill, nor does it vest judges with a mandate to try to remedy every social problem. When this court rushes in to remedy what it perceives to be the failings of the political processes, it deprives those processes of an opportunity to function."

" . . . The solution to this seemingly intractable problem is to defer to the political processes, unpalatable as that may be to some."

To Brennan, on the other hand, the court "would not be faithful to our obligations under the 14th Amendment" if it applied so "deferential" a standard to the distinctions drawn by elected officials.

"If the state is to deny a discrete group of innocent children the free public education that it offers to other children residing within its borders, that denial must be justified by a showing that it furthers some substantial state interest. No such showing was made here."

In legal terminology, the dispute is over "levels of scrutiny" applied by the courts to actions by government, to whether states need just a "rational" reason for its distinctions between illegal aliens and others or "substantial" justifications.

While Brennan's view prevailed Tuesday, Burger's has been dominant over the last few years and is expected to dominate further if President Reagan, who share's the chief justice's approach, has a chance to replace one of the five justices in the Plyler vs. Doe majority.

So it is unclear whether Plyler vs. Doe will survive, let alone be extended to welfare, food stamps and other benefits now denied illegal aliens. The illegal aliens case was about education, Brennan stressed, not other "mere" benefits.

Justice Lewis F. Powell, Jr., on the other hand, said in a footnote that "if the resident children of illegal aliens were denied welfare assistance, made available by government to all other children who qualify, this also--in my opinion--would be an impermissible penalizing of children because of their parents' status."