The more all-encompassing a designation, the harder it is for a stereotype to stick.
So today, let's look at what exactly comprises "The GOP."
As opposed to the Democrats (which are more of a loose single-issues confederacy), the GOP is a triumvirate of three major factions: The religious right, Big old business, and Tea.
Big old business is the smallest and wealthiest. I also call it big old to distinguish it from major businesses in general. ((Most actual conglomerates hedge their bets by donating money to both parties, but older companies either have a public face that leans more to the right, or major executives who publicly do so. That's why we think of Oil or pharma as right-leaning with tech and media on the left. They're all playing both sides against the other.))
B.o.b. puts up with the Religious right (though they butt heads if their sales involve vices) mostly because they need the rank & file and the local level control and donations. But their boat gets rocked by Tea too much for them to really get along with them.
The religious right was the largest for a while, but has been outnumbered by Tea in recent years. They've got a lot of state-level and below workings, small donations and probably still the largest volunteer base. They're also ground zero for the social conservatism of the party in general.
((And yeah, it's usually both rural and some flavor of Christian. Remember an earlier post when I said go back far enough in history and you'll find out why things happen the way they do? A few generations ago, a huge percentage of the RR were farmers and related professions. That's a profession where you can do everything right, prepare as much as you possibly can, and die anyway. A drought, frost, or blight you have dick-all control over can and does kill you and everyone you know and love. That said, failing to do all you can and prepare as much as possible will kill you more easily. Rural communities lean towards conservatism because trying radical new ideas that haven't been proven is quite literally increasing the odds against you in a bet that you and your family won't starve. So yeah, they take a long time to embrace change of any sort. That's because doing so is the reason their grandparents survived to adulthood. So lighten the fuck up on them.))
Tea and B.o.b. both get along with the RR (B.o.b. for their manpower and resources, Tea for a lot of shared fiscal beliefs), but the RR's constant beating of the social conservatism drum irritates more than it brings agreement.
The last is Tea. It's the youngest and largest current faction, but it hasn't managed to turn that into a complete takeover. Most are aware that overreaching is a bad idea. ((Tea has its roots in the old Reform Party, which split the GOP vote enough for a Democrat presidential win in back-to-back elections back in the 90's)). Tea can be more or less described as a "get shit done" faction. They're not quite Objectivist as Rand thought of it. Belif in less government is not a belif in no government. They're usually more of the, "hey, building code enforcement is great. But that TSA is sucking up money and not accomplishing shit. Let's shut them down and take their stuff."
Unfortunately, they butt heads with RR over social conservatism a lot and the libertarian ideals of a lot of them cause smaller scale grumblings among B.o.b.
So yeah, keep in mind that A) they still manage to work together, but B) don't have enough of a united front for themselves, much less crossing the aisle, but C) until one of them overtakes the other two, it's likely to be that way for a while. Of course, D) the one most likely to overtake is Tea, which is also the easiest to reach across the aisle in any meaningful way.