How about an exhaustive list of groups who claim to be Christian and you say are not.
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Mormons, Jehovah’s Witnesses, Christian Science, Unitarian universalists, oneness Pentecostals (deny Trinity), Christian Identity Movement .
In short it comes down to something simple. All Christian churches agree on the basics, - the Trinity and the person work and nature of Jesus Christ (which includes Grace over works). The rest of things Christians fight over aren’t matters of Salvation.
Of course, what about the churches who by doctrine say exactly what you claim is the minimum requirement but who allow homosexual marriage and appoint homosexuals to the ministry? Are people who are members in such a church or denomination disqualified even though they have a good conservative track record?
Then, you mention works parenthetically. As I understand it, Catholics believe we are saved by Grace alone and must respond with faith which is only shown by our works. Does that mean you agree with their doctrine sufficiently that you would vote for a solid conservative Catholic?
And what about those folks who are not part of any denomination? Do they need to fill out a theological questionnaire even if they've been a solid conservative for decades and have a track record to prove it?
I'm really sick of the fine people who meet all the appropriate religious criteria for the religion first crowd to vote them into office but in return do nothing about mass murder and the elimination of every Christian symbol that is an intrinsic part of this nation. It's time to judge people on their record and if they insist on going to Hell themself but help to turn the country around, so be it. Going after the single lost sheep is all well and good, but millions of sheep are being slaughtered every year and the tests the religion first folks have been applying haven't helped to stop it.