@theminkim Some schools once had a religious affiliation but don’t anymore. Others still have an official officiating but religion isn’t a strong part of the campus vibe.
Examples:
Liberty University is going to be mandatory chapel and strong Christian influence.
Baylor is voluntary chapel services but middle of the road for a Christian college.
Georgetown is a Catholic University (Jesuit) but many students are not Catholic and still consider Georgetown regardless of religious affiliation.
SMU has a reputation of being a somewhat preppy school for rich kids but the Hunts and Presidential Scholars come from all backgrounds. I would worry more about whether you fit in the student body profile than Methodist in the title. Whether you are a fit is a personal question that can only be decided with a visit when school is in session.
Good luck in your search! You will have great options if you are NMF. You will need to apply to schools before you know Finalist status.
Two other schools not mentioned are Univ. of Arizona and Arizona State. Not sure how close to full ride. I think Arizona waives OOS fees for NMF. My D would have been a net cost of a few thousand per year if she had decided on U of A as a NMF who qualified of in state tuition.