This is kind of true even outside America.
The reason is that "liberals" tend to be less authoritarian and more democratic than conservatives.
So "liberal" parties in a democracy tend to allow more expression of diverse opinions inside and outside the party that also often generates heated open (public) debates. This may sometimes seem like in-fighting. And sometimes it does become so when people become too emotional about some issue. But this is seen as normal and healthy - the ability to be comfortable with different opinions and maintain a relationship with someone who may have some different views is considered an important attribute to have in a multi-cultural society and a democracy.
In fact, this kind of "in-fighting" is sometimes even seen in the legislative houses of democracies (especially in younger non-western democracies). Some examples:
- British Parliament fight is full of 'dodgy' language
- Slaps, Punches, Uproar: When Parliament, State Assemblies Turned Into House of Ruckus
- The world's biggest parliamentary brawls
Due to the nature of democracy to allow different opinions, such occasionaloccasional flare-ups of emotions are actually considered normal.
Conservative parties on the other hand tend to be more authoritarian, and dissent or deviation from the party leaders public political stands is often seen as an attack on the party leadership itself. Thus, in conservative parties divergent views are actively discouraged or only shared and discussed in private.