And to answer the question of the original poster, nothing has changed in regards to the NIC fraternities since Alpha Phi Omega's founder Frank Reed Horton was simultaneously active in both Sigma Alpha Epsilon and founding Alpha Phi Omega. (Eight of Alpha Phi Omega's Fourteen undergraduate founders were in the Lafayette College chapters of Sigma Alpha Epsilon, Five were in a local Fraternity called Krescents which about a year after Alpha Phi Omega was founded became a chapter of Kappa Delta Rho (and one independent))
In thirty years of brotherhood in Alpha Phi Omega (including time on Public Relations committee and Alumni committee), I have *never* heard of a student organization (much less a GLO) in the United States for which membership in Alpha Phi Omega prevented membership in that organization. I *have* seen GLOs which did not allow students to join both their GLO and Alpha Phi Omega *in the same semester*, but frankly, that counts as belief that students shouldn't fail out rather than discrimination.
TL;DR: No Fraternities (social or otherwise) care.
Because "undergrads, please abandon your national policies and make something up" will end well