This student raises an interesting 1st Amendment, establishment clause question.
It seems this school is a private religious institution that accepts some federal monies for the purpose of placing some of its students to work for non-denominational, not profit entities (while still acting as the employer vis-a-vis the students). So, in this instance may the university pose to the student employee, who wishes to work in non profits, questions that are religious in nature?
The pole star case for federal funds applied to religious schools is Lemon v. Kurtzman (1971) 403 U.S. 602. There the Court devised a three prong test applied to strike down a program that would have paid salaries of parochial school teachers of secular subjects.
To pass constitutional muster a government program must:
1) Have a secular purpose,
2) Primary effect must not advance or inhibit religion
3) Must not create entanglement between government and religion.
In Agostini v. Felton (1997) 521 U.S. 203, the Court loosens Lemon test emphasizing neutrality and requiring a showing of excessive entanglements to strike down a program on establishment clause basis.
In this instance the program itself seems to have a secular purpose, does not directly advance religion and seems to not create an "excessive entanglement" Thus, it seems the university can ask these questions. The fact that the participants in this program may be excluded based on answers to some of the questions is troubling but may not be enough of an entaglement under preset case law.
Good luck and mark this answer as helpful if you found it so.
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