I guess it would depend on what you mean by "conflicts". If you mean simple differences in practices among adherents to the same branch, that is one thing. On the other hand, if you mean serious rifts over those differences, that's another thing entirely.
Generally speaking, the less importance a given branch places upon observing Torah law, the less in-fighting there is within the group about how that law is to be interpreted. After all, one normally does not contend for that which one finds unimportant.