And now that I finished this ep for a second time, I'm not even sure if Kinsey is supposed to be a red-blooded Republican. He has elements of stupidity and close-mindedness from both parties.

I think that to an extent you may be right, but I think that there is a difference between Kinsey and a truly fiscally conservative Christian. Kinsey, like most politicians, is a slimey worm. He wants to be portrayed as a real traditional family guy, but really that's just his image to get elected. He's exploiting the truly good founding values of the US, which, let's be honest, some Republicans (and Democrats too!) do.
I think that, as a whole, SG-1 has a real respect for life, freedom, and good old "American values," as well as Christianity and all other modern religions. I really think the writers were criticizing politicians and ignorance as a whole, rather than just conservatives. Their respectful portrayal of the military, usually more conservative than not, is a testament to that I think.