I've been reading all the comments below, and not one mentions the third largest, and most cohesive, branch of Islam. A faction whose guiding principle is to integrate into the local community, aiding and improving it with no "missionary" zeal to convert it to Islam.
Any idea of which innocuous branch I am writing?

For contrast the Christians stopped a lot of their infighting when they decided to just identify as Christians first and not as a specific denomination. There are exceptions of course but that allowed them to come together as a single force here in the US.

I think it’s a mistake to believe that there is such a thing as a universal Islamic philosophy of conquest. Just like Christianity, there is no universal interpretation of Islam. I have travelled and lived in Muslim countries, such as Malaysia, and never found the majority to be anything other than welcoming and kind, and pretty tolerant of other religions. As you have pointed out, just as in Christianity, there are sects and schisms. There are fundamentalists in both religions too, and there are those who would kill members of an opposing sect just as quickly as those of a different faith or none. The current jihadists hate anything liberal or progressive and modern, and want to halt and even regress the advances of the last 2000 years. That is except when technology such as the internet and mobile phones help them to advance their pernicious ideology! That isn’t so different from the fundamental Christians trying to return us to biblical times either, is it? The thing is, the clock can not be turned back....once the genie is out of the bottle it can’t be squeezed back in again. It is fanciful at best to think that Islamic State or any other group will ever be able to wipe out the civilisation of the last two millennia. They can however, create havoc and sow fear amongst us, but it’s up to us not to allow that to happen.