Frankly, when it comes to state run institutions I cannot argue with you. Exclusions such as the ones we're discussing do not belong there since the entire body of all walks of life are contributing and thus should be able to benefit from this institution. However, regarding private institutions... those are funded and founded on unique principles. These unique principles do not need to conform to anyone other than those that are leading and funding the institution.
Yes, federal guidelines such as those in the constitution and it's amendments must be adhered to. In this case, the primary guidelines of the first amendments are protecting these private institutions rather than the other way around. Freedom of religion being the primary one and right to assemble another.
One group coming together centered around a particular set of values does not exclude others from doing so as well.