Cognitive Dissonance: Laissez Fair Capitalism vs Democracy

In a perfectly-efficient laissez faire capitalist society, everyone works toward their own economic self-interest. So long as contracts are enforced and property is protected, this is functional because economies of scale are not a zero-sum game; if each citizen was highly productive, and each was as productive as the next, everyone could be rich.

However, in a political game that is zero-sum, where the government is willing and able to redistribute money from one group and give it to another (meaning that someone winning means someone else losing), everyone serving their own self-interest will lead to an equilibrium where the person(s)/group(s) with the most influence seek to take as much as they can from the rest of society without suffering backlash.

What are the implications here? Does a pure capitalist economy coupled with a pure democratic political system necessarily lead to two sets of disagreeing values, one economic and one political, in the citizens? Would the citizens of such a society move toward an equilibrium between the two ideologies, or lean more toward one or the other? Is it functional to do so? Is it morally correct to do so? Would one part of the society naturally stratify itself according to its members' wealth/income, and another part do the opposite? If so, what would happen to the middle class/middle ground, and would civil war/rebellion/revolution be unavoidable?