So yeah! The District Court for the Northern District of Illinois said: "Title II's prohibition of religious discrimination is consistent with this modern recognition that stereotyping on the basis of religious belief or the lack of belief in God is unwarranted."
Welsh v. Boy Scouts of America, 742 F. Supp. 1413, 1434 (N.D.Ill. 1990). The Seventh Circuit affirmed on a different basis and declined to reach the constitutional question.
Welsh v. Boy Scouts of Am., 993 F.2d 1267 (7th Cir. Ill. 1993),
cert. denied 510 U.S. 1012, 114 S. Ct. 602, 126 L. Ed. 2d 567 (1993). The dissent in the CoA opinion noted that the majority left that particular question unanswered:
The majority's interpretation of Title II would leave the Boy Scouts and other like organizations free to discriminate not just against atheists--or those whose beliefs arguably conflict with the group's most central philosophy--but against anyone at all on sheer whim. Under the majority's analysis, a group such as Rotary International or the Jaycees or Little League is, absent a more comprehensive state statute, perfectly free to exclude blacks, Jews, Catholics, etc. Rather than unduly narrow the reach of Title II, I would hold that the statute does prevent discrimination by membership organizations. This does not necessarily mean that the Boy Scouts could be forced to admit atheists, however, because the First Amendment protects organizations from having to accept those who do not share its most elementary beliefs. Id. (Cummings, J., dissenting)
Long story short, outside of the Northern District of Illinois, nobody knows. Hooray!