"This case does not require us to determine when a con dition placed on university funding... becomes an unconstitutional condition. It is clear that a funding condition cannot be unconstitutional if it could be constitutionally imposed directly... the First Amendment would not prevent Congress from directly imposing the Solomon Amendment's access requirement, "
The direct decision may not have been affected by the new conservatives on the court, but under the previous judges the stated rationalle--and thus the precedent set--could have been different. It might well have sought to cement federal supremacy.
BTW, out of curiosity, if a decision is 8-0 but the primary decision is supported by four judges and a concurrence by the four others, what determines precedent?