The underlying split is that the right wants a homogenously united community while the left is united in the acceptence of their differences. This makes me wonder why the right doesn't want communism. Could this be like homosexuality, that the right secretly wants it and just doesn't dare to say it?
I'm not even sure capitalism is the right word, at least not in the US. I'd almost describe their ideology as neo-feudalism.
The republicans have always paid lipservice to the idea of meritocracy, of an even playing field, and fair competition. But that isn't what we're seeing from them - they're merging economic and state power in a way that serves to lock in the existing class structure and remove what little social mobility remains. They may pay lipservice to the idea of a free market liberal democracy, but that isn't the government they're creating.