Right there with you being stunned. I think it's one of two things...
1. What they get is more important to them than what they need to give. You wonder how any Christian or veteran could support Trump, but it's simple; their hate for liberals/minorities/whatever grossly outweighs their love for god and/or country. The extreme mental gymnastics come naturally once that occurs.
2. It's a skillset, or a lack thereof. Same as how you or I would probably make terrible pilots or doctors without a lot of training, these people are terrible at recognizing the obvious. They're the reason why the Nigerian Prince scam is still profitable.