I hope I'm not too late to answer this.
I went to DePaul. You do have to take 1 religion course, so I took Hinduism. There is nothing overtly Catholic about the university except for the church on campus (easy to walk past and ignore). Well, if you read the DePaul literature they talk about how the Vincentian order is important to the mission, blah, blah, blah, but you don't encounter it in The Theatre School at all. It's never mentioned; you're never expected to attend mass... You don't even get Easter off if a show is in performances.
As far as the program, it's trial by fire, conservatory style. You stage manage for 4 years. If you want to do other crews (lights, sound, etc.) you have to seek it out. You do have to take tech/design classes, but you can choose what they are after 1st year. The only downside is business, acting & directing classes are not required, but you can fit them in if you want. I managed to take pretty much any class I wanted.
Because it's a BFA program, you do have to take general ed requirements, hence the religion course. I think it's also 1 science, 1 math, 1 history, 2 english, and something else.