Scalia first made his views on the subject known in National Endowment for the Arts v. Finley (524 U.S. 569 (1998)). In that case, Scalia [EDIT: concurred in holding that making "decency" a consideration in the awarding of NEA grants did not violate the first amendment. He argued further that the NEA could engage] in content discrimination when giving out it's grants. He wryly noted that were the NEA's actions upheld, "Avant-garde artistes such as respondents [would] remain entirely free to epater les bourgeois; they are merely deprived of the additional satisfaction of having the bourgeoisie taxed to pay for it." He continued then to argue that it is absurd to equate a lack of taxpayer subsidization with an effort to suppress unpopular ideas. And he specifically claimed that "The nub of the difference between me and the Court is that I regard the distinction between 'abridging speech' and funding it as a fundamental divide, on this side of which the First Amendment is inapplicable....The government, I think, may allocate both competitive and noncompetitive funding ad libitum, insofar as the First Amendment is concerned."
Horowtiz thus inquires:
What relevance should this position have for Justice Scalia in cases involving public funding of religious programs, or public funding of non-religious activities carried out by religious groups? Does this suggest Justice Scalia believes it is constitutional to impose conditions on such groups -- for instance, that no money flowing to such a group be spent on anything that may contain religious content, or that a religious group receiving government funds may engage in x religious speech but not y religious speech? This is not a gotcha post; commenters are welcome to discuss the ways in which Justice Scalia is or is not consistent in his views on this point. But I think it's an interesting subject for musing and discussion.
What with the controversy over President Bush's "faith-based initiatives" and the desire amongst some to make sure these funds only are distributed to groups that meet certain non-merit-based requirements (not discriminating against homosexuals, for example), this is an issue that will eventually come up. So what's the end result?
It's not an exact fit, but the closest case we have in explicating Scalia's views is the recent case of Locke v. Davey. There, the Supreme Court upheld a Washington law in which college scholarships could not be used by students studying theology or other religious vocational training. The Court specifically allowed the possibility that Washington could, if it wished, grant the scholarships (in other words, the discrimination was not constitutionally compelled), however, it said that Washington was equally free not to. Since the decision was discretionary, I think it is safe to say that Washington made its decision based on some presumably distasteful or negative quality of theological training (either that funding it breaches the separation between Church and State, or that theological training is not something the state wishes to foster, or some other reason--it really doesn't matter what).
Scalia dissented quite forcefully from this decision. He argued that
When the State makes a public benefit generally available, that benefit becomes part of the baseline against which burdens on religion are measured; and when the State withholds that benefit from some individuals solely on the basis of religion, it violates the Free Exercise Clause no less than if it had imposed a special tax.
In other words, he was not very much swayed by his previous argument in Finley--that nobody is being stopped from pursuing theological training, they are just deprived of the pleasure of having the secular state subsidize it as well.
Perhaps the analogy might best be understood with regard to Lee v. Weisman. If Locke represented the state privileging a secular viewpoint without providing an equivalent for (but not prohibiting the private expression of) a religious choice, then Lee represents the reverse--the state privileging a religious viewpoint (in this case a graduation prayer) without providing an equivalent secular choice (but not prohibiting the private expression of secularity, by letting the student either stay home from graduation or not join in the prayer). In Lee, the Court held this dualism to be unconstitutional--persons of dissident religions should not be put in a "participate or protest" dilemma, and that it is unfair to effectively kick them out of public activities if they do not adhere to the dominant religious sensibilities. It would be absurd to respond that the dissident student could have her own, private graduation with her own prayers (or lack thereof) and that this would make the First Amendment problem just go away. Instead, it is sufficient to note that the state cannot publicly put religion and non-religion (or majority religion and minority religion) on unequal terms--it must either provide equal opportunity to all, or abstain from the endeavor entirely.
This would mesh very well with what Scalia is saying in Locke--but for the fact that he dissented vigorously in Lee. In Lee he proclaimed the long standing tradition of religious prayers (it should be noted that the Locke statute was in accordance to a long standing provision of the state constitution) and derided the notion that participation the religious portion of the ceremony in any way coerced their assent to religious dogma. This is merely "respect for religion" that the government is perfectly permitted to foster in the public sphere--the student, as noted above, is still perfectly free to believe what he wants in private. Why then cannot the state ask its citizens to be secular in public and in public funding (in accordance with its popular mandate), and abide by whatever religious sensibilities it has in private? It seems that Scalia cannot make sense of his Locke argument given his sweeping dismissal of the logical vein in Lee (one other argument Scalia might use, that religious views gain higher protection than "mere" speech also falters via Lee--Scalia specifically labels the two equivalent: "The government can, of course, no more coerce political orthodoxy than religious orthodoxy.").
I should note that I agree with Scalia when it comes to Locke--I think it was wrongly decided and that it represents state-sponsored discrimination against religion. But that's because I take the broader view of what state-sponsorship means--the view that Scalia rejected for both free speech (Finley) and freedom of religion (Lee) cases. I do not think that Scalia is being consistent here, nor do I think he even realizes he's being inconsistent. But Scalia's religion clause jurisprudence has always been--ironically, since he is one of the loudest critics of this supposed ailment in our legal tradition--among the most incoherent and non-cohesive on the Court.