You are misinformed, the piece of the puzzle you missed is that Mohamad stated that there is only one true Islam, his. All other branches of Islam are apostates and must be killed. This set all branches of Islam at odds.
They were not fighting for ‘moderation’, but survival. Islam, like a biker bar respects only strength. If any sect succeeds in convincing the others by their strength that they are the prophesied final Caliphate, you will see Islam reach ‘critical mass’. The 90 % of ‘moderates’ will become radicalized almost overnight.
Having lived amongst Muslims for a decade, I know of what I speak.
“Mohamad stated that there is only one true Islam, his. All other branches of Islam are apostates and must be killed. This set all branches of Islam at odds.”
Not to mention Mad Mo wrote that all things belong to Allah and anyone that states differently are to be killed. Tolerance for those that are not muslims only goes so far in that they must at some time convert or be killed. Mad Mo took an incremental approach to this as to appear to be kind.