I haven't read Sowell but is this what he means by a 'hybrid ideology'? My impression of Marxists is that they view the world through both lenses and believe #1 can be achieved when #2 is solved through revolution or other means.

Isn't that the opposite of what Marx believed? His world view was that a perfect society (communism) would arise when virtually all institutions were abolished, because in his view, the imperfections of human nature were all caused by "alienation" which itself came from the capitalist system.

Actual communists tended to start out living that creed: they'd systematically destroy any existing institution. But then they'd find society didn't work at all without them, so they'd pretty rapidly build new institutions, that all happened to be controlled by them.

Conservatives on the other hand are, by their nature, conservative about changing things. They tend to regard existing social structures as evolved and thus encoding great wisdom, even if it can't be easily articulated. To change those institutions is thus highly risky, even if it may not be immediately apparent why that is. This is the opposite of Marxism, which is a utopian ideology in which changing everything at once is not too much.

A Conflict of Visions is not a book about Marxism, it is a description of a model to help us understand our ideological preferences. Like all models, it is wrong but sometimes it is useful.