Folks, the US Constitution says absolutely nothing about marriages. (Reference: http://www.house.gov/Constitution/Constitution.html) It's entirely a state matter, unless Congress passes a law about it (which then may or may not be constitutional.)

That having been said, if the wording of the contract does not specifically state that the so-called domestic partners must be of the same sex, I can't imagine you wouldn't have a sound legal case. Although the intent was probably to provide coverage for those whom would normally get left out (i.e. gay partners), I doubt that there was any kind of "inept moral judgements on [your] belief system." It sounds like an oversight, not an intentional slight toward you; insurance companies are notorious for refusing coverage for the stupidest reasons -- it's just part of the mindset.

I suggest a talk with your union representative. You probably have a relatively painless and cheap arbitration process that will be much easier than trying to convince the insurance company yourself or hire a lawyer.