You’re not the first to make such observations. To quote Barry Goldwater (Republican party nominee for US President in 1964):
> Mark my word, if and when these preachers get control of the [Republican] party, and they're sure trying to do so, it's going to be a terrible damn problem. Frankly, these people frighten me. Politics and governing demand compromise. But these Christians believe they are acting in the name of God, so they can't and won't compromise. I know, I've tried to deal with them.
Was he describing America or Iran? Hard to figure out as we seemed to be in War due to similar people in control of another (not)important country :)
It was about America. I think the only overlap between "conservative" Republicans and religious fundamentalists is the "social conservatism", e.g., "family values", "law and order", etc. The quotes are because there's debate about what those terms really mean.
The key difference is that religious fundamentalists pledge their allegiance to the Church, not the country; not "God" either (although they might claim it to be so). They are tribal to their core and anybody outside their church is an "other" and is not worthy of being considered a fellow citizen.