The center of the left doesn't disavow it's extreme. The left realizes that the political is downstream of the cultural, and so their advocates proliferate their message via the culture, knowing adherents will pursue the political on their behalf. The left understands that in a "war of ideas" there is no defenders advantage, the only correct maneuver is an attack. The left, at it's most extreme, is willing to expend physical bodies in furtherance of an agenda. The left is hierarchical, they fall in line and they wouldn't dare second guess their priestly classes. The left cultivates communities, and engages in social outreach, and couches their ideology in language that appeals to the ethos of people. The left isn't plagued by larping, cultural stagnation, and a lack of imagination. Furthermore they will engage in their heterodox opinions rather than dismiss them without consideration simply on the basis of them being heterodox.
Most importantly, the left owns "progress", which is inevitable and unstoppable. Fighting progress is a fools errand. What matters is the direction of progression. Are progressing TO or FROM Christ? The Right needs to learn to guide progress, like one digs a canal.