I think this, and other internal fighting, illustrates how the GOP isn't one homogeneous group but rather a coalition of groups with often very different approaches to the world.
So it's not really right to say Republicans are the problem for an instance like this since it's an attack on a Republican.
I don't know if Ann Coulter identifies as a conservative, but if anything it's more like conservatives are the problem. Not all Republicans are particularly conservative.
But really I think it's more that shock jock commentators like Coulter are the problem as they lob these grenades to get attention.... which we give to them, playing into their games.