“Perhaps I’m missing something...”
No, I think your instincts are right on.
There is also the party that champions the corporate equality of its constituents, that does not acknowledge God-given rights, that champions the subjugation of the rights of non-constituents to constituents, that champions freedom from responsibility at the expense of innocent parties whose personhood (and therefore whose right to due process) is denied to facilitate their destruction, that champions immediate gratification and discourages individual accomplishment. This party champions Eminent Domain and the supremacy of The State, unmitigated abortion on demand for any reason, homosexuality - essentially, any form of depravity that will appeal directly to the basest desires of the human human in exchange for party loyalty.
I can't really distill it down further than that. Each person - including a few on this very thread - has to evaluate in his or her own heart where he (she) belongs, and which party best represents his (her) beliefs. Naturally the party that champions human rights is going to have its share of those who acknowledge the Creator as the great Bestower of those rights. If folks are uncomfortable with that, they might consider going elsewhere. For those of us who love American and believe her ideals to be both noble and immutable the Republican Party, for all her warts, is the best vehicle forward.