Looking at the dichotomy between "right" and "left", and seeing that the left is truly violent while the "right" is incredibly passive, some thoughts came to mind.
Why is the left violent? Because that is their philosophy, at its core. The world is unjust, and so "we" must do something about that. What can be done? Their answer is to tear down all institutions of power. They think that anyone who is stronger than them is a threat to them. And so they lash out wildly against anyone and everyone, endlessly. Whatever the problem is -- it's not the left, it's everyone else!
Why isn't the right violent? Because that is their philosophy at its core. The world is unjust, and "we" must do something about that. What can be done? Their answer is that by rightly living, they can ease and perhaps even end some of the suffering. They think that they have some power and that they must use that power wisely. Anyone stronger than them isn't necessarily a threat, but a potential partner or ally. And so they seek to reconcile and arbitrate disputes.
I don't see how these two philosophies will ever reconcile. The left is a cancer that the right has created by its passivity and reconciliatory nature. And leftists who take two moments to think seriously will always end up in the right.
I think you're more talking towards the progressive v. conservative divide, where the progressives are trying to push society "forward" while the conservatives want to put on the brakes. The right way to deal with progressives is not conservatism, it is to eliminate the progressives and roll their changes back.
Fundamentally, the idea that has spoiled the pot in America is that if we simply take care of ourselves and don't do evil that society as a whole will do just fine. That's simply not the case. We must be aggressive and active in propelling society in a positive direction, and when there are people pulling it in the opposite direction, we must not simply resist, but eliminate them as threats to the whole.
For instance, the right way to deal with marxism is not to debate them. It's to throw them out of helicopters. It's to drive them into the woods and then burn them down. You don't make peace with an enemy who doesn't acknowledge your most basic human rights. You thoroughly defeat them on the field of battle and piss on their graves.