WASHINGTON, D.C. — The U.S. Supreme Court’s new term, starting Oct. 4, returns to its standard routine: hearing arguments in person and taking on hot-button issues.

The big cases, among the 34 it has so far agreed to hear, include those on abortion, the Second Amendment, and religious liberty issues related to a death penalty case and religious schools excluded from a state school choice program.

The nine justices are jumping into the fray at a time when the public’s perception of the court is becoming more negative.

A Gallup poll released two weeks before the court’s new session said only 40 percent of Americans approve of the job the court is doing, compared with 49 percent two months ago and 58 percent a year ago.

“Not since Bush v. Gore has the public perception of the court’s legitimacy seemed so seriously threatened,” said Irv Gornstein, executive director of the Supreme Court Institute at Georgetown University Law School referring to the Supreme Court’s decision settling the 2000 presidential election.

Likely the most anticipated case of the term is Dobbs v. Jackson Women’s Health Organization, the abortion case that will be argued Dec. 1 and has been described as potentially taking down Roe v. Wade, the court’s 1973 decision legalizing abortion.

Here, the justices will consider the constitutionality of a Mississippi state law prohibiting abortions after the 15th week of pregnancy. The state ban was struck down by a federal District Court in Mississippi in 2018 and upheld a year later by the New Orleans-based U.S. Court of Appeals for the 5th Circuit.

The nation’s high court already stepped into the abortion debate in early September when it declined to block a Texas law banning abortions after six weeks of pregnancy. About three weeks later, Texas abortion providers urged the high court to again review their challenge to the state law before a federal court’s anticipated ruling on it in December.

In previous abortion rulings, the Supreme Court has consistently said states cannot restrict abortion before 24-weeks of pregnancy, focusing on viability, or when a fetus is said to be able to survive on its own. If the court sides with Mississippi in this term’s case, it would be the first time it would allow an abortion ban before the point of viability and could lay the groundwork for other abortion restrictions.

Catholic leaders and pro-life organizations have shown support for the Mississippi law in friend-of-the-court briefs. The U.S. Conference of Catholic Bishops, in its brief, stressed that abortion is not a right created by the Constitution and warned that if the court “continues to treat abortion as a constitutional issue,” it will face more questions in the future about “what sorts of abortion regulations are permissible.”

The court also is taking up two death penalty cases. On Nov. 1 it will look at an issue it has previously weighed in on: the presence of religious leaders at an execution. But this case will specifically examine exactly what a spiritual adviser can do during an execution.

The focus is on the case of John Ramirez, a Texas death-row inmate who was granted a stay of execution by the Supreme Court in early September based on his rejected appeal for his pastor to pray over him, with his hands on him, in the execution chamber.

The court has looked at spiritual advisers accompanying inmates during executions four times in recent years in court orders with differing opinions based on specific circumstances.

In one of its rulings in 2019, it allowed the execution of an Alabama Muslim to proceed even though the inmate had appealed the state’s decision to deny an imam’s presence at his execution. Two U.S. bishops said the court’s inaction was “unjust treatment” that is “disturbing to people of all faiths.”

This year the court will also hear a government appeal to reinstate the death penalty for Boston Marathon bomber Dzhokhar Tsarnaev. It will review a lower court’s decision that said errors made by the judge in Tsarnaev’s trial tainted his sentencing.

A point of interest in this case, initially filed by the Trump administration, is that the Biden administration is continuing with it despite President Joe Biden’s anti-death penalty platform during his election campaign.

Krisanne Vaillancourt Murphy, executive director of Catholic Mobilizing Network, said if Tsarnaev’s death sentence remains overturned, he would never leave prison. His execution, she said, “would bring little healing to those he harmed and would serve only as state-sponsored vengeance.”

Another big case, that similarly echoes previous ones, is the Dec. 8 oral arguments in Carson v. Makin, where the court will determine if Maine violated the Constitution by prohibiting students from using funds from a state school choice program for schools that provide religious instruction.

In a similar case last year, the court ruled in Espinoza v. Montana Department of Revenue that states are not required to subsidize private education, but they can’t exclude religious schools from receiving tuition funding simply because they are religious.

The USCCB praised the Espinoza decision, saying it “means that religious persons and organizations can, like everyone else, participate in government programs that are open to all.”

This term, the court also will look at handgun laws, reviewing a New York law, upheld by the lower courts, that requires individuals to have a license to carry a concealed gun outside the home.

The U.S. bishops have not weighed in on this case but they have spoken out against handguns in the past, arguing that they should be accessible to those in law enforcement and the military, but that all others should have significantly restricted access.

The court also will take up two immigration cases involving immigrants who were ordered to be deported but claimed they were entitled to humanitarian relief and can’t be deported to their home countries because they could be tortured or persecuted there. They have argued that after spending more than six months in immigration detention awaiting the resolution of their claims, they are entitled to a hearing before an immigration judge.

With all of these cases in the wings, Supreme Court watchers have expressed concern over the court’s current ability to find general consensus or narrowly decide cases as it did in previous term.

Also, people will be paying close attention to Justice Amy Coney Barrett, who will be starting her first full term.

Even though the new term is just beginning, the justices were hardly on hiatus in the summer months when they issued a number of decisions in what’s been described as the shadow docket.

These decisions used to primarily focus on specific issues such as death penalty emergency orders but in recent weeks they extended to broader issues such as immigration, evictions, COVID-19 and abortion.

Also in the weeks prior to the court’s new term, three of the justices — Barrett, Clarence Thomas and Stephen Breyer — spoke in public about the court’s role, stressing that decisions the justices make are not political.

But that’s not how everyone views the current court.

Gornstein, who spoke at a Sept. 21 online preview of the court’s new term, said: “It is all well and good for justices to tell the public that their decisions reflect their judicial philosophies, not their political affiliations.”

But he argued that it’s hard to see otherwise, noting: “If the right side’s judicial philosophies always produce results favored by Republicans and the left side’s judicial philosophies always produce results favored by Democrats, there is little chance of persuading the public there is a difference between the two.”