The conservative side can never win. By definition. Conservatives are simply fighting for what progressives supported 20 years previous. It's like saying that you can win a war by slowing down the enemy front. You simply get overrun. You have to oppose the enemy with enough force to push it back. Conservatives push nothing.
The kind of conservatives you're describing are the kind that are not very conservative, and even if they are, don't do much about it. And you're saying all conservatives are like that ("by definition.") Well, obviously, people like that aren't going to win much of anything. But why would those be the only kind of conservatives?
We all like to complain (rightly so) about that kind of conservative. That might even describe most 21st-century American "conservatives" when it comes to most issues. But those people don't define the word. I get the feeling you just want to lash out at them, and my comment was a convenient punching bag.
What we need to save America is a new progressive reform movement. American politics are broken, so it seems pretty hopeless.
Our politics is broken because our people are broken. Fixing the people is what you're referring to as a culture war. You can't have reform or progress without fighting the culture war. In fact, that's why conservatives have been failing to conserve anything or "push" anything. It's because the Left has been waging a sustained culture war for several decades, and the Right is either not trying, or just not very good at it.