It's legitimate. It plays soccer against the University of British Columbia, and wins, which would be rather hard for a mill to do. http://www.athletics.ubc.ca/ It's a Roman Catholic university, and has been accused of "discriminating on the basis of sexual orientation": http://www.bccla.org/othercontent/00twusccfactum.html
Trinity Western is conservative Protestant and most of the Bible boys on degreeinfo would feel very much at home there. It is a well respected school. The group licensing teachers in BC refused to license TWU on the grounds that there would be an inherent bias against homosexuals because of their rules. Note that heterosexual activity, outside of marriage, is also forbidden.
I sit corrected. I misread a sentence that said "Redeemer Pacific College [...] is a Roman Catholic College located on the campus of Trinity Western University, Canada's largest private Christian liberal arts university." (http://www.esli-intl.com/rpc.htm)
I used to know someone who went to Trinity High School in Illinois, who claimed that they actually used the school cheer, "Father, Son, and Holy Ghost Here's to the school we love the most. Trinity, Trinity, Yay."