But is this ideological inhomogeneity in the USA a cause or a consequence of the political system?

It's a good question, and the polarizing effect of political parties certainly does work the way you describe.

That said, I do think the rural/urban divide in the US is a real split in terms of the kinds of public services and private contributions different communities value and expect, and the political parties have exacerbated that rather than created it.

Regardless, I agree with your main point about the polarizing effects of bicamerality.