The Supreme Court. (Alex Brandon/AP)

The Supreme Court begins a new term Monday with the most important civil rights agenda in years on the horizon and amid intensified scrutiny of the relationship between Chief Justice John G. Roberts Jr. and his fellow conservatives.

If last term’s blockbuster cases involving immigration and President Obama’s Patient Protection and Affordable Care Act centered on the reach of the federal government’s powers, this term offers a chance to cast the 21st century meaning of the Constitution’s guarantee of equal rights.

A combination of cases asks the court to decide whether special protections and accommodations for minorities have reached their limit and whether society’s growing acceptance of same-sex unions warrants constitutional protection.

The justices will consider the continued viability of affirmative action in college admissions when it hears a challenge next week to the University of Texas’s race-conscious selection process.

And there are several challenges awaiting the court’s action on the most controversial part of the Voting Rights Act — the Civil Rights-era requirement that some states with a history of racial discrimination receive federal approval before enacting voting or election-law changes.

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The court seems all but certain to confront the issue of same-sex marriage by considering suits against the 1996 federal Defense of Marriage Act. The law’s provision denying federal recognition of same-sex marriages performed in states where they are legal has been deemed unconstitutional both by the Obama administration and lower courts that have considered it.

In addition, the court will be asked to review a decision that overturned California’s Proposition 8, in which voters amended the state constitution to define marriage as between a man and a woman.

A decision on whether to accept the gay rights cases is likely to come in November.

The cases could keep the court in the same bright public spotlight that shone on its deliberations last term.

This term opens with questions about the unity of the five Republican-nominated justices who since 2006 have had a remarkable impact on the court’s jurisprudence: striking down campaign finance regulations, approving federal restrictions on abortion and expressing doubts about government programs that make distinctions based on race.

“I think there’s no question this Supreme Court is the most conservative in our lifetime,” said Georgetown law professor Michael Seidman. “But there is a question about what kind of conservatives they are.”

In the most important cases of the upcoming term, Justice Anthony M. Kennedy is likely to resume his role as the pivotal justice.

But the greatest intrigue will surround Roberts, who, in the most important case of his tenure, sided with the court’s four liberals last June to affirm the constitutionality of Obama’s signature health-care act.

Kennedy and Justices Antonin Scalia, Clarence Thomas and Samuel A. Alito Jr. pointedly signed a 65-page dissent that described the decision as “a vast judicial overreaching.”

Roberts billed it as just the opposite, an exercise of judicial modesty and deference to the political branches that requires “every reasonable construction must be resorted to, in order to save a statute from unconstitutionality.”

Amid reports that Roberts had changed his mind and his conservative colleagues were furious — reports that seemed to have come only from the justices or those close to them — the reaction from the right was brutal.

“Privately, nobody thinks of Roberts the same way,” said Curt Levey, who heads the conservative legal group Committee for Justice.

Others say the Roberts’s decision was surprising, but that the reaction has been overblown.

“I don’t think everything you knew about John Roberts is no longer true,” said Paul Clement, the former George W. Bush administration solicitor general who argued the health-care case for the challengers. “I think 99 percent of it still is.”

Steven Teles, a political scientist at Johns Hopkins University who wrote a book, “The Rise of the Conservative Legal Movement,” said the unique nature of the health-care case makes it hard to draw greater lessons about Roberts.

It is extremely rare, Teles said, for the Supreme Court to be asked to strike down the major achievement of a sitting president who is about to enter a reelection campaign.

Roberts’s decision reveals more of how he views his role as chief justice, Teles said. “Roberts wanted to limit or cripple the ACA [Affordable Care Act] as much as possible consistent with preserving the legitimacy of the Court. And I think he did that.”

Others think the issues teed up for this term — particularly those involving race — are of more concern to Roberts than those of last term. Since he was a young lawyer in the Reagan Justice Department, he has been sharply critical of government-sponsored racial preferences. “It is a sordid business, this divvying us up by race,” Roberts wrote in a 2006 dissent in a redistricting case.

“I think this is an issue the chief justice really and desperately cares about,” said Pamela Harris, who worked in the Justice Department in the Obama administration and is now a visiting professor at Georgetown.

“In the health-care case, the chief justice — and I’m not saying this was intentional or anything like that — he built up some kind of legitimacy capital for the court,” she said. “My hunch would be that where he would want to invest it is in the race cases.”

Roberts has not discussed the decision publicly and has largely stayed out of view this summer.

And as they are wont to do when there is criticism from the outside, justices on both the right and left have circled the wagons.

Scalia, who has given numerous interviews this summer as he promotes a new book, has downplayed any tension.

“You shouldn’t believe what you read about the court in the newspapers,” Scalia told CNN. “No, I haven’t had a falling out with Justice Roberts.”

Justice Ruth Bader Ginsburg warned an interviewer from Reuters: “Don’t ask me if the chief switched sides.” Thomas went to great lengths during a session at the National Archives to talk about how the justices get along even when they disagree.

And the newest justice, Elena Kagan, told a University of Michigan law school audience that “there is not a single member of this court, at a single time, who has made a decision, who has cast a vote, based on ‘Do I like this president, do I not like this president . . . will this help the Democrats, will this help the Republicans?’ ”

The justices, she said, disagree and move on. The advice she got early on, Kagan said, was that taking things personally would make for a “long life tenure.”