What it boils down to (on top of outright bigotry) is deflection: the Christian right wants to impose religion as the law of the land, so of course they accuse Muslims of wanting to do this instead to distract people.
Be fair. The vocal religious right aren't actually Christian, they just claim to be when they're on TV (or the internet). Just like with 'radical Islamic terrorism' (where most of the terrorists aren't actually practicing Muslims, or they wouldn't be doing what they're doing). I think that's an important distinction to make.
Their idea of "Christian" is to be white. They protest shariah, to protest Islam. They protest Islam to protest brown people.