As two pro-Israel lobbyists near trial on charges of trafficking in classified information, a federal judge is preparing to grapple with some thorny questions, such as what to ask potential jurors about their religion and whether it is legal to knock jurors off the case based on their perceived religious affiliations.

At a hearing last month, Judge Thomas Ellis III asked lawyers for the defense and the prosecution to submit legal briefs on whether it would be proper for either side to remove jurors with “obvious” Jewish or Arab names.

“In other words, can the government strike someone just because his name ends in stein, or whatever, or can the defense strike somebody because his name is Mohammed?” Judge Ellis asked. He said there is no clear federal legal precedent on the point in the 4th Circuit, which includes his Alexandria, Va.-based court.

The defendants, Steven Rosen and Keith Weissman, are former employees of the American Israel Public Affairs Committee. The pair, who have pleaded not guilty, are charged with relaying classified information to journalists and foreign diplomats, including Israeli officials.

The Supreme Court ruled in a 1986 case, Batson v. Kentucky, that the Constitution bars prosecutors from removing potential jurors based on race, and that prosecutors had to give a race-neutral reason when challenged over the use of a so-called peremptory challenge against a particular juror. In 1994, the court put similar rules in place against excluding jurors based on gender.

However, the Supreme Court has never ruled on whether the rationale of the race- and gender-based cases extends to religion. In 1994, the court turned aside a case from Minnesota in which state courts accepted a prosecutor’s removal of a juror who identified himself as a Jehovah’s Witness. Justice Thomas complained in a dissent that his colleagues were trying to dodge the logical consequences of their rulings on the basis of jurors’ race and gender.

A prominent defense attorney and advocate for Israel, Alan Dershowitz, acknowledged there are diverging court rulings on the issue, but said it makes little sense to bar the use of race and gender in jury selection, while permitting use of religion.

“It seems to me you have to have religion as a part of Batson, otherwise it is a denial of equal protection … especially since being Jewish is not just a religion but also an ethnicity,” Mr. Dershowitz said.

The Harvard Law professor said a Massachusetts court rejected a challenge he brought to a prosecutor removing jurors with Jewish-sounding names. The court ruled that, due to intermarriage, the excluded jurors might not actually be Jewish, which Mr. Dershowitz said was beside the point. “It didn’t matter whether they were Jewish, it was what was in the mind of the prosecutor,” he said.

Judge Ellis’s demand for briefs on the issue could put the government in the awkward position of defending its right to exclude Jewish jurors just days before the opening of a trial many Jewish groups view with suspicion.

However, the defense seems most intent on probing jurors’ religious views. In a court filing last year, defense lawyers proposed giving potential jurors a broad-ranging questionnaire asking about their religion and frequency of attendance at religious services, as well as their race, “ethnicity,” and political party affiliation. Prosecutors argued that the questions were inappropriate because they might make jurors think those attributes were relevant to judging the case impartially.

“It is unfortunate that bias and prejudice on the issue of religion still exists,” the defense attorneys, Abbe Lowell and John Nassikas, wrote. “However, it is true that a number of people when confronted with this case will have a pre-judged idea about Aipac, its relationship with Israel, and the allegations in this case that Jewish-Americans shared national defense information with Israeli officials.” The lawyers said seeking jurors’ religious views would help ferret out such bias.

It is possible defense attorneys might use the questions about religion to decide to retain jurors who are Jewish, or even evangelical Christians who are increasingly pro-Israel. “There’s no violation in keeping people. There’s only a violation in striking them,” Mr. Dershowitz said.

The trial of Messrs. Rosen and Weissman has been delayed repeatedly as the parties battled over the use of classified information in the case. Last week, Judge Ellis mentioned a possible trial date of March 25, which would be more than two and a half years after the men were indicted.

Judge Ellis’s comments on the issue of jurors’ religion were first reported by an online newsletter, Secrecy News.