Duke, as a private institution, is not an arm of the state like UNC, so has more latitude in enforcement. We went through something similar in Indiana last year with RFRA, and that law would have a potential impact on students the minute they walked off campus at Notre Dame, or Butler or any other private institutions in the state. As the OP specifically said they are concerned about inclusion in terms of LBGT issues, this is a relevant consideration.
More substantively, for a student with high need, Grinnell is the least expensive option, and Grinnell is a community and institution which is committed to socio-economic, racial, ethnic, LGBT inclusion. The President of Grinnell is a gay man, married, with children. I, and others, have encouraged the OP to research the options rather than, as the OP has stated they are trying to move away from, simply getting carried away by prestige and reputation.
What is the best choice for this student? With close faculty mentoring, phenomenal resources for student funding for research, internships, travel abroad, Grinnell could be a great option. Of course, Duke is a superb school. The question is, where will the OP flourish, academically, personally, without financial burden. Only the OP can decide that.