A new Fox News poll shows Democrats, Republicans and independents generally in agreement on the criteria of characteristics, professional background and ideological affiliations President Obama should consider or not consider when selecting a new justice.

When asked about the nominee being a woman, 77 percent of Democrats, 87 percent of Republicans and 87 percent of independents agreed that it "shouldn't matter." The nominee being "a minority" drew similar results, and smaller but still robust majorities said it shouldn't matter if the nominee was "a homosexual."

About half of Democrats, Republicans and independents agreed that the nominee's being an attorney, a judge or a constitutional scholar should be "a factor" -- not the "single most important" factor, nor an unimportant one. There was some disagreement on the question of whether the nominee went to an Ivy League school or a "less elite, everyday American law school": A plurality of Republicans preferred the latter, while a plurality of Democrats and a majority of independents said it made no difference.

Those of all all political affiliations agreed that it would not matter if there were no justices with a "Protestant religious background" (John Paul Stevens was the only remaining Protestant on the court), and all were comfortable with the nominee being a Mormon or a Christian "who takes the Bible literally."

Respondents were not comfortable, however, with the idea of a Muslim, atheist or "socialist" on the Supreme Court. Thin majorities of Democrats and independents said they were comfortable with a Muslim, but fully 66 percent of Republicans said they were not comfortable. Republicans were also overwhelmingly opposed to an atheist or "socialist," while Democrats and independents split about evenly on the former and Democrats split evenly on the latter. All parties agreed they were comfortable with a libertarian on the court.

The poll surveyed 900 registered voters nationwide last week, with a 3-point margin of error.