WASHINGTON — The Supreme Court opens its new term Monday with a fall lineup of cases that includes how to deal with violent threats on the Internet, the role of religious liberty in prisons and whether working women who are pregnant have a right to lighter duties on the job.

Rather than split the court along sharp conservative versus liberal lines, these initial cases will require the justices to clarify the law where it is murky. In one colorful case involving a boat captain accused of obstructing an investigation by dumping his catch into the ocean, the justices will debate whether dead fish can be treated as the legal equivalent of shredded documents.

The major ideological conflicts are waiting just off stage, however. Later in the term the court is likely to take up a same-sex marriage case and decide whether states must give gay couples an equal right to marry.

The partisan divide over voting rules has also reached the Supreme Court in emergency appeals from Wisconsin and North Carolina. The justices will decide in next week or two whether these Republican-led states may enforce new rules.

Wisconsin wants to require its registered voters to show current, government-issued photo identification cards, even though critics warn it might bars thousands from casting ballots.

In North Carolina, a federal appeals court blocked new rules that ended same-day registration and barred the counting of ballots cast in the wrong precinct. The judges, both Obama appointees, said the changes would violate the Voting Rights Act and discriminate against blacks. The state’s lawyers filed an emergency appeal last week asking the justices to revive the rule changes.

The abortion issue could also return later in the term. Arizona wants to enforce a law that limits when women can use drugs to end early pregnancies, but the law was blocked by a federal appeals court in California.

Last week, Texas won an appeals court ruling that allows it to enforce a strict law that shut down most of the state’s abortion clinics. The law said these clinics must meet all the standards of an “ambulatory surgical center” and their doctors must have admitting privileges at a nearby hospital.

More than 20 years ago, the Supreme Court said states may regulate the practice of abortion, but may not put an “undue burden” on women seeking to end a pregnancy.

Other highlights include:

• Religion and prisons: Does a Muslim prisoner have a right to grow a beard? Arkansas prison authorities said no, contending inmates can hide dangerous objects in beards. (Holt v. Hobbs, Oct. 7)

• Undersized fish: Does the obstruction-of-justice law that forbids destroying documents or “any tangible object” include small red grouper? John Yates, a boat captain in Florida, was accused by a federal agent of having illegally caught grouper that were under 20 inches. But before returning to shore, he dumped the small fish and was charged with obstruction of justice. (Yates v. U.S., Nov. 5)

• Racial gerrymander: Did Alabama’s Republican-led Legislature violate the Constitution’s guarantee of the “equal protection of the laws” when it moved 120,000 black residents into already majority-black election districts? Black lawmakers and Alabama Democrats said this “racial gerrymandering” would dilute the voting strength of the state’s black residents. (Alabama Legislative Black Caucus v. Alabama, Nov. 12)

• Threats and free speech: Does a Facebook poster have a right to rant about his ex-wife and imagine the “ways to kill you,” including to “dump your body off” in a creek and “make it look like a rape and murder”? It is a crime to transmit “any threat” to injure another person, and Anthony Elonis was convicted because a “reasonable person” would see his rant as a threat. But the court will hear his free-speech claim that government must prove that he intended to threaten her. (Elonis v. United States, Dec. 1)

• Pregnancy discrimination: Must employers make special accommodations for pregnant employees? Federal law forbids discrimination based on pregnancy and says such women “shall be treated the same” as other employees. United Parcel Service refused to exempt Peggy Young, who was pregnant, from the normal duties of lifting 70-pound packages. Federal courts rejected her discrimination claim on the grounds she was treated the same as other workers, but the justices will hear her appeal and decide whether pregnant workers must be given the same special accommodation as other employees who have a temporary disability. (Young v. UPS, Dec. 3)