I think both parties are pretty diverse in this sense, but there tends to be a lot more public infighting on the Republican side than on the Democratic side.
It's sort of like two dysfunctional families. The Democrats are the family that merely tolerate each other out of common self interest or obligation, but have little to no connection and rarely communicate with each other, and just try to push their agenda behind the scenes, even if it hurts another member in the coalition. On the other hand, the Republicans are like the family that you see screaming at and beating their child in public for having a temper tantrum (or in the case of real life, shutting down the government). This only further fans the flames of the rivalry.
