President Bush’s reported decision to scratch all men from the short list of candidates for the most recent Supreme Court nomination is stirring debate and disagreement among staunch opponents of affirmative action.

Some view the alleged constraint as perilously close to the kind of quotas and set-asides Mr. Bush has denounced, while others contend that the president should have ample leeway to consider race, religion, and gender as he attempts to shape the high court.

“I think it’s quite inappropriate for the search for a new appointment to the Supreme Court to be oriented by sex. Sex has nothing to do with that role,” a philosophy professor who opposed racial preference programs at the University of Michigan, Carl Cohen, said.

In a radio broadcast on Tuesday, a conservative Christian leader with close ties to the Bush administration, James Dobson, said he was told by Mr. Bush’s chief political adviser, Karl Rove, that Mr. Bush insisted that his latest selection for the Supreme Court be female.

Mr. Rove “made it clear that the president was looking for a certain kind of candidate, namely a woman, to replace Justice O’Connor,” said Mr. Dobson, a clinical psychologist and founder of a Colorado-based ministry, Focus on the Family. “And you can imagine what that did to the short list. That cut it.”

“I haven’t looked at who I think might have been on that short list, because Karl didn’t tell me who was not willing to be considered, but that may have cut it by 80% right there,” Mr. Dobson said.

During a briefing yesterday, the White House press secretary, Scott Mc-Clellan, was not asked about Mr. Dobson’s assertion that Ms. Miers’s gender was a prerequisite for the nomination. A spokesman for Mr. Bush did not return a call seeking to confirm the claim.

“I’m troubled if he’s actually set aside a slot for a person of a particular ethnicity or for a female,” a vocal opponent of many affirmative action programs, Linda Chavez, said. “It’s not the same as a meritocratic decision supposedly made on objective measures. Nonetheless, if you restrict your pool to only looking at women and minorities, it certainly is a problem for an administration that ostensibly does not believe in preferences,” she said.

Ms. Chavez, a former aide to President Reagan who now heads a group that fights quotas and preferences, the Center for Equal Opportunity, said she senses that gender is becoming a larger part of the White House’s defense of Ms. Miers. “It seems they are falling back on ‘This was a woman,'” Ms. Chavez said.

Ms. Chavez said she appreciates that political considerations might have played a role in selecting Ms. Miers. “None of that justifies picking this particular woman,” the former White House aide said. “I think there were a lot of qualified Hispanic and female candidates. I’m not sure Harriet Miers would have come to the top of my list.”

Another leading critic of affirmative action efforts, Abigail Thernstrom, said the ethics of college admissions and day-to-day government hiring are not applicable to a Supreme Court pick.

“I don’t think that this is a quota issue or a set-aside issue. It’s closer to ticket balancing, in that it’s making a political appointment considering your constituents,” said Ms. Thernstrom, a senior fellow at the Manhattan Institute. “I have no objection on the grounds of high principle to the president thinking, ‘Gee, we’re getting down to one [woman. It may not be a great idea for me to appoint another white male.’ It gets very complicated because Hispanic probably trumps male,” she said.

Ms. Thernstrom labeled as inaccurate reports that all the female finalists besides Ms. Miers opted out of further consideration. “I know it’s not true that all the strong women candidates withdrew from consideration. I’m not going to name names, but I’ve been in touch with some of them, and they didn’t withdraw,” Ms. Thernstrom said.

Ms. Thernstrom, who was appointed by Mr. Bush as vice chair of the Commission on Civil Rights, said presidents have always used key appointments to appeal to racial and religious groups. “If Hillary puts Barack Obama on her ticket, that isn’t a racial double standard, that’s trying to reach out to a constituency,” Ms. Thernstrom said.

At a news conference last week, Mr. Bush seemed to indicate that gender was not a factor in his decision. “I picked the best person I could find,” he said. However, during the same exchange with reporters, the president made more than a dozen references to Ms. Miers as a woman and repeatedly noted that she achieved a number of firsts for female lawyers in Texas.

Another member of the civil rights panel, Jennifer Braceras, said she believes Mr. Bush inoculated himself against the charge that he was setting aside a female seat when he initially named a white man, Chief Justice Roberts, to the spot being vacated by Justice O’Connor. “I don’t think there should be a Jewish seat, a black seat, a female seat, which was actually the beauty of President Bush’s selection of John Roberts to fill the O’Connor seat in the first place. He sort of put that myth to bed,” Ms. Braceras, a visiting fellow with the conservative think tank Independent Womens Forum, said.

Ms. Braceras said it was “perfectly appropriate” for Mr. Bush to consider race and gender in the nominating process, but she said those concerns underscored the need for the president to select someone whose qualifications were unquestionable. “If you’re going to make an appointment based on race or gender, you want to have a really qualified person, so you’re not accused of just having a quota,” she said.

Ms. Braceras, a Republican, said the nomination of Ms. Miers did not meet that standard. “I think this was a huge political blunder. No constituency is happy.”

The Michigan professor, Mr. Cohen, rejected the idea that race or sex should be a part of the president’s political calculations when making key appointments. “It’s totally inappropriate to weigh their sex, just as it is totally inappropriate to weigh their color,” he said.

Asked if the process described by Mr. Dobson ran afoul of Mr. Bush’s stance against quotas, the professor said, “Is it an inconsistency? Yes, it is.”