Personally, what shocks me more than individuals getting elected, are the educated individuals who believe it. I work in an office filled with engineers. Amazingly, my first cubicle neighbor, and I've found he isn't an outlier, was a diehard young earth creationist. Electrical engineer, 4 year degree at a good school. Still somehow believes in a vast conspiracy by scientists in league with the devil to hide The Truth. At a previous company, another engineer, this one with a PhD, was not ashamed of the time he berated guides/curators at the Museum of Natural History for a display on dinosaurs.
I attended such a church until my early 20's (I'm 32 now) and around elections there were many sermon reminders that they needed to go vote for people aligned with their conservative values. At my former church they wouldn't explicitly endorse candidates, but it was understood you voted Republican. If the Republican at least appeared to be an evangelical Christian, you would get more support. (I remember George W. Bush being called a "man of God" by several people.)
Moreover, if you had an inclination to, say, vote Democrat, then you better be quite about it. People would just about question how "true" of a Christian you were if you did that.
Disclaimer: I know that not every church in states like Texas are like this. I know because I went to less political churches too. (I don't go to church anymore for what it's worth.)
Couple that with post-election apathy towards what's going on in Austin, and you get crackpots. Not saying that some people don't specifically vote for creationists, but my limited experience tells me most do not.
Churches can lose their tax-exempt status for doing that. It happened to a church in upstate NY during the first Clinton election. (They later had the ruling overturned on the basis that the IRS somehow singled them out for disproportionate treatment, but I'm hopeful that with more evidence of more churches doing it, simply getting caught wouldn't be legitimate grounds for crying "They're picking on me!" any more...)
I live in Texas. I've yet to see or hear of this really happening. I've seen churches directly involved in politics my whole life. Sure, they try not to mention names, but they don't need to.
Not coincidentally, religious influence in government is one of the factors that has been slowly leading me to question the merits of democracy in general.