A lot of worms for sure. However, perhaps one reasonable test might be whether or not the institution trains its student's to practice a specific faith. Liberty's motto of "Training Champions for Christ since 1971." seems like their objective is a religious one. If Congress isn't to "make no law respecting an establishment of religion, or prohibiting the free exercise thereof." it seems that spending tax dollars on a organization in order to train champions for Christ would be a conflict. I think a religious institution can perform non-religious services, and that those services might be subsidized by the government, however, when the service is to advance the religion, the government should not help or hinder the organization. There is little doubt in my mind that if Liberty were an Islamic institute, the call for the separation of Church and State would be vociferous.