A series of lower court rulings, reflecting what now seems like a hygone liberal judicial era, confronts the increasingly conservative Surpreme Court that opens its 1981 term Monday.

The first full Supreme Court term of the Reagan era will review important lower court decisions affirming the rights of prisoners to petition the federal courts, the rights of mental patients to refuse drug treatments, the right of illegal aliens to a free public education, the rights of the mentally retarded to be free of shackles and the right to sue the president.

At a time when the prevailing political line is to "get the federal government off the backs" of local officials, the justices will debate the actions of federal judges who threw out a small town's ordinance to restrict the sale of drug paraphernalia, overrode another town's ban on children hanging around amusement arcades, struck down a state legislature's determination that only American citizens should be hired as probation officers and nullified an article of the Texas constitution.

Speculation about Supreme Court decisions is hazardous. But it is safe to say that simply by being at the court this term, many of these rulings are in jeopardy.

To the extent that Justice Sandra D. O'Connor's views are known, she is unlikely to come to the rescue. In fact. some of these cases seem tailored for her arrival. If O'Connor, a former state legislator and state appellate judge, champions any cause at all, it is the prerogatives of the states.

These decisions are among 102 accepted for review this term by last term's court. Another 20 or 30 will be announced Monday. Those already chosen over a broad range of subjects:

* Rights of Aliens: One of the court's most highly publicized cases stems from a 5th U.S. Circuit Court of Appeals decision that illegal alien children in Texas are entitled to a free public education under the 14th Amendment's equal protecton clause. Texas school districts are in a panic over the decision, written by legendary southern judge Frank Johnson, since it will force them to absorb thousands of additional children at public expense. Beyond that, a Supreme Court affirmation of the decision (Plyler vs. Doe) could open up to illegal aliens many more of the privileges now reserved for citizens and foreigners legally in this country.

The court will review a California ruling striking down a ban on hiring aliens as probation officers. (Cabell vs. Chavez-Salido).

* Rights of the Institutionalized: Two appeals court rulings under review significantly expanded the rights of mentally retarded and involuntarily committed mental patients in state-run facilities and, in the view of state officials, created a "staggering" potential for lawsuits and interference with the professional judgments of physicians and hospital officials.

One appeals court ruling (Youngberg v. Romeo) prohibited the much-critized Pennhurst Home for the retarded in Pennsylvania from shackling or otherwise physically restraining patients without demonstrating a "compelling necessity" to prevent violence. The other, (Mills vs. Rogers) from Massachusetts, gave involuntarily committed mental patients the constitutional right to refuse treatment with psychotherapeutic drugs.

* Rights of Criminal Defendants: The most celebrated criminal case before the court is that of former Green Beret doctor Jeffrey MacDonald, who was convicted of murdering his pregnant wife and two children at Fort Bragg, N.C., in 1970. The 4th U.S. Circuit appeals court reversed the conviction because of long delays in bringing MacDonald to trial.

Potentially more important are several cases that the court could use to limit the access of prisoners to the federal courts. Each year, inmates who have exhausted their original appeals file thousands of habeas corpus petitions with the federal courts, raising every conceivable legal argument, in an effort to get out of prison. The proliferation of such petitions has been a target of Reagan administration low-and-order advocates, of state officials who resent the intrusion of federal judges in their criminal justice systems and of Chief Justice Warren Burger, who said in a speech last year that these "endless appeals" undermine inmates' incentives to rehabilitate and the "finally" of the criminal justice process. One of these cases (Rose vs. Lundy) involves a federal court ruling in favor of a man serving 120 years for rape and sodomy who had not exhausted his claims in the state courts when the federal courts intervened. Another (Engle vs. Isaac) asks the justices to rule that prisoners may not raise objections to their convictions that they failed to raise at their trials.

In a major death penalty case (Eddings vs. Oklahoma) this term, an Okalahoma youth convicted of the unprovoked murder of a highway patrolman has asked the court to ban the death penalty for juvenile criminals.

* First Amendment Rights of Expression, Association and Religion: An elections law case (Common Cause vs. Schmitt) could have a major impact on the growth industry of politics -- independent expenditures. The court has been asked to restore a $1,000 independent-spending limit declared unconstitutional by lower courts as a burden on free political expression.

A Missouri lawyer, disciplined by the bar for departing from its restrictions on lawyer advertising, gives the court the opportunity to say just how tightly such professional advertising can be controlled by professional organizations (In Re. R.M.J.)

In another Missouri case (Widmar vs. Vincent), students who were blocked by the University of Missouri from using taxpayer-financed facilities for their own religious services have asked the court to rule that they should be treated like any other campus organization.

Princeton University is before the justices this term (Princeton vs. Schmid), defending its ban on the use of its facilities for propagandizing by "outsiders," in this instance, the U.S. Labor Party.

A new First Amendment right -- that of children to play games in amusement arcades -- is before the justices. The city fathers of Mesquite, Tex., banned those under 17 from the arcades, saying that they wanted to discourage truancy, among other evils, though the ban was enforced round the clock. The 5th Circuit Court of Appeals, acknowledging that the Supreme Court had not spoken on this subject, struck down the ordiance, saying the age restriction "unconstitutionally trammels fundamental personal rights" of social association (City of Mesquite vs. Aladdin's Castle, Inc.).

* Executive and Congressional Power: The justices once again consider whether the president can be sued by damages for violating individual rights. Last year, the court split evenly in the wiretap case of former Richard Nixon national security aide Morton Halperin because Justice William H. Rehnquist disqualified himself. This year Rehnquist is expected to participate in a case brought by Ernest Fitzgerald, the one-time Pentagon whistle blower who sued Nixon and presidential advisers after his job was eliminated.

Government lawyers will also try to convince the court that federal agency officials should not face personal damages suits for alleged failures to enforce federal law. The case (Velde vs. National Bank Police Assn., ) stems from a charge that the Department of Justice failed to punish local Law Enforcement Assistance Administration grant recipients who practiced discrimination. The issue takes on special relevance in light of the Reagan administration's softening of enforcement under a number of similar laws.

The court is expected to enter the "legislative veto" controversy, though the case has not yet been accepted for review. The issue (Ins vs. Chadha ) is whether Congress can give one house the power to veto actions of the executive branch.

* Doctors: the court will review the legality under antitrust laws of fee schedules for doctors (Arizona vs. Maricopa County Medical Society ) and of American Medical Association restrictions on physician advertising (AMA vs. FTC ).