Those values, as demonstrated by your list, are political values, having nothing to do with religion. It's completely appropriate to discriminate on that basis, however, Americans are supposedly free to worship as they like and not be discriminated on the basis of their religion. Cain would also seem to be in violation of Title VII of the Civil Rights act:
Title VII of the Act, codified as Subchapter VI of Chapter 21 of 42 U.S.C. § 2000e  et seq., prohibits discrimination by covered employers on the basis of race, color, religion, sex or national origin (see 42 U.S.C. § 2000e-2). Title VII also prohibits discrimination against an individual because of his or her association with another individual of a particular race, color, religion, sex, or national origin. An employer cannot discriminate against a person because of his interracial association with another, such as by an interracial marriage.
I can't help wondering if Muslim were replaced wth Christian in that sentence, what the result would be?