WASHINGTON – Sex. Immigration. Guns. Abortion. Religion. Executive power.

Pirates, even.

That's the menu so far for the Supreme Court's new term, which Monday begins an extended run through much of the 2020 election season. Before the justices adjourn next June, their influence will be felt by tens of millions of Americans, including President Trump and Congress.

Democrats' demands for documents and testimony pertaining to the president's personal and business finances already were working their way through lower courts when Trump's dealings with Ukraine turned the buzz in the nation's capital to impeachment.

All of those skirmishes will produce battles over congressional subpoenas and administration claims of executive privilege that could reach the high court. And if the House follows through, Chief Justice John Roberts would preside over a Senate trial.

"It is likely the court will get involved in some way, where they can’t avoid doing something that’s going to be controversial," says David Strauss, who heads the Supreme Court and appellate clinic at the University of Chicago Law School.

It's been only a year since Associate Justice Brett Kavanaugh's razor-thin Senate confirmation, a triumph for conservatives that was overshadowed by decades-old allegations of sexual misconduct that he denied. Now that Kavanaugh and fellow Trump nominee Neil Gorsuch have settled in, those conservatives want to see results from a court rebuilt in Trump's image, with a 5-4 conservative majority.

Did it help last term? Not so much: The bloc of liberal justices prevailed in as many divided cases as their conservative counterparts. Just as often, the voting patterns were mixed. Gorsuch, the Coloradan confirmed in 2017 to a seat President Barack Obama was blocked from filling, displayed an unpredictable libertarian streak. Kavanaugh sought a low profile by sticking with the majority more than others. Roberts switched sides with regularity.

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"It was a bizarre and strange and inexplicable term," Lisa Blatt, an appellate lawyer who has argued more cases at the Supreme Court than any other woman, said last week.

Thus it was that Trump lost his effort to add a question on citizenship to the 2020 census when Roberts didn't buy the government's proffered rationale. Similar doubts surround the administration's reasons for seeking to end a popular Obama-era program that gives undocumented immigrants brought to the United States as children clearance to remain and work. It's not even clear Trump wants to end the program if he wins the high court's blessing.

The future of the Deferred Action for Childhood Arrivals (DACA) program highlights the court's November sitting. First, though, it will hear arguments Tuesday on whether gay, lesbian, bisexual and transgender workers are covered by a federal civil rights law barring sex discrimination. In December, the justices are likely to tackle gun rights. Abortion will be on the docket early next year.

"This is a confident court that has not shied away from taking on the most polarizing issues," says former U.S. solicitor general Gregory Garre. "But even for this court, that is going to be a sensitive task."

From gays to guns

The justices will waste no time diving into a divisive issue:Gay rights.

Three cases will test whether the 1964 Civil Rights Act, which bans job discrimination on the basis of sex, applies to gay and transgender workers. The answer will be particularly important in 28 states that do not have their own protections.

The cases pick up from where the same-sex marriage battle left off in 2015, when the court ruled 5-4 that states cannot ban gays and lesbians from getting married. But the author of that decision and others favoring gay rights, Associate Justice Anthony Kennedy, retired last year and was succeeded by Kavanaugh, whose vote will be key.

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In an effort to win over at least one conservative justice, lawyers for two gay men and a transgender woman fired from their jobs claim to be following the plain text of the law. Were it not for their sex, the theory goes, they would have kept their jobs.

Employment discrimination is a "rampant problem," Paul Smith, a frequent Supreme Court litigator who won a major gay rights case there in 2003, said recently. Another such victory, he said, "would be huge for the LGBT community."

In November, the justices will hear a two-year-old dispute between Trump and Democrats in Congress over the fate of nearly 700,000 undocumented immigrants brought to the United States as children.

The program was established in 2012 without congressional approval, enabling recipients to avoid deportation and get work permits. The administration first announced its plan to wind down DACA two years ago, but it was blocked nationwide by federal judges from California to New York.

The court's willingness to hear the case signals a potential win for the White House, but how it wins would be crucial. If the justices say Trump has the same discretion to end the program that Obama had to create it, a future president just as easily could renew it. If they agree with the Justice Department that it's unlawful, Congress would have to step in.

"The government has no fewer than seven different arguments" for the court to let it end the program, Georgetown University Law Center professor Martin Lederman said recently. "The government only has to win one out of seven to win this case."

The court's date with gun rights, scheduled for December, could go by the boards if gun control advocates have their way.

The case focuses on New York City's somewhat extreme restriction against transporting legally owned guns beyond city limits. The justices agreed in January to hear a challenge from gun rights groups, but the city and state wiped the regulation from the books in hopes of getting the case dismissed.

The problem for gun control groups is that the justices would be free to hear a different case in the near future, including one aimed at winning the right to carry guns in public nationwide. Since establishing the right to possess guns at home for self defense a decade ago, the court has refused to re-enter the debate. In the meantime, lower courts have upheld most state and local restrictions.

"If they say this case is moot, there are other cases available in line," Paul Clement, a former U.S. solicitor general representing gun rights groups in the New York case, said recently.

Abortion and religion

After dealing with gays, guns and immigration, the justices might be pining for a lower profile. But a topic that has haunted the court since 1973 looms.

The court agreed on Friday to hear a major new abortion case from Louisiana, which wants to implement a law requiring providers to have admitting privileges at nearby hospitals. The justices struck down a similar law in Texas three years ago, but Kavanaugh has replaced Kennedy, who was the deciding vote.

More abortion cases from Indiana, Illinois and elsewhere are lurking. All deal with restrictions imposed by states, ranging from demands placed on patients or providers to flat-out bans on abortion after or even during the first trimester of pregnancy.

Last term, the court upheld an Indiana law requiring the burial or cremation of fetal remains following an abortion, but it refused to consider that state's effort to ban abortions based on sex, race or disability.

Less likely to win the justices' consideration are laws working their way toward the high court from Georgia, Ohio, Missouri, Kentucky, Arkansas, Mississippi, Alabama and elsewhere that ban most abortions. Those laws more clearly conflict with the high court's precedents.

"It’s hard to imagine the chief justice seeing anything good from issuing an important, substantive abortion ruling," says Neal Devins, director of the Institute of Bill of Rights Law at William & Mary Law School.

Another high court precedent could fall if the justices issue a major ruling in a Montana case testing whether state funds can be used to help pay for tuition at religious schools.

Parents of religious school students sued for access to a program providing tax credits for tuition assistance. Residents and businesses that donate to private scholarship organizations receive up to $150 in tax credits; the donations are used for scholarships for low-income families.

A district court initially ruled for the parents, but the Montana Supreme Court said it conflicted with the state constitution and invalidated the entire scholarship program.

The high court has ruled in favor of religious liberty in several cases recently. In June, it ruled 7-2 that a mammoth Latin cross on government land in Bladensburg, Maryland, does not have to be moved or altered in the name of church-state separation. The justices also have allowed public prayer at government meetings and some public funding for religious institutions.

If it rules in favor of religious school funding, the court might overrule a 1990 precedent upholding laws that apply to the general public even if they restrict religious freedom.

Blackbeard's Law

Additional cases on the court's docket raise issues of racial discrimination, political corruption and, once again, the Affordable Care Act, which the justices upheld in 2012 and 2015. The latest case involves Congress' decision to withhold promised payments to insurance companies.

But perhaps the most unusual case involves a copyright dispute over a sunken pirate ship captained 300 years ago by the legendary pirate Blackbeard.

That case, to be heard in early November, pits North Carolina against a video production company documenting the salvaging of the shipwreck Queen Anne's Revenge, which ran aground in 1718 and was discovered in 1996. The state, which is being sued, passed a statute to convert the salvage effort to public record.

It's name: Blackbeard's Law.