It seems pretty blatant to me that Senate Democrats are not going to consider this in their judicial deliberations,
"The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." (from Article VI of the United States Constitution)
Senate Democrats have admitted they will only approve nominees who support Roe v. Wade to the federal judiciary. The Catholic Church considers abortion to be wrong, therefore serious Catholics are ineligible, by Democrats' standards, to serve as judges.
Senators may disagree with William Pryor on his interpretation of the law, but unless they find that he does not believe in upholding the Constitution (which is not the same thing as supporting Roe v. Wade), their vote against his nomination is an unconstitutional vote. Special interest groups like People for the American Way and the ACLU would be well-served by taking off their ideological blinders when they read the Constitution.
(link via locdog's blog. Joshua Claybourn has similar comments as mine too)