As an American, I'll try to explain how our two parties (and their voters) work in practice.
The Left (voters) have two main platforms: economic and cultural.
The Right (voters) have two main platforms: economic and cultural.
The Left votes for the Democratic Party. The Right votes for the Republican Party. Independents mostly vote one way or another, and a small percentage vote for whoever seems most moderate that particular election.
When governing, the Democratic Party works with the Republican Party to implement:
1. The cultural platform of the Left.
2. The economic platform of the Right.
The cultural platform of the Right and the economic platform of the Left are not implemented.
The Left calls the Democratic-Republican Establishment the "corporate" party and believes the country has moved strongly to the Right over the last 40 years. (They are focusing on the fact that the economic platform of the Right is being implemented.)
The Right calls the Democratic-Republican Establishment the "uniparty" and believes the country has moved strongly to the Left over the last 40 years. (They are focusing on the fact that the cultural platform of the Left is being implemented.)
This is a stable political system because neither a Left voter nor a Right voter wants to vote for the other party, because then they wouldn't even be getting half of what they want! The Democratic-Republican Establishment doesn't care who people vote for, because it wins either way. The important thing is for voters to believe their vote matters—even though it actually doesn't.
The key result is that neither the Left's economic platform nor the Right's cultural platform are ever implemented. (A few legacy cultural issues on the Right, e.g. 2nd Amendment gun rights, still exist. Same with pre-WW2 economic issues on the Left.)
Hope this helps!