If muslims aren’t killing Jews and Christians they are perfectly content to kill other muslims.
Left to their own devices they would just keep killing everyone until the only two humans left in the world were two mulims.
Then one of them would kill the other one.
Kurds are not all Muslim. It depends on where they are as to the extent of that statement.
In Iraq, very high percentage of Muslim, except for Nineveh which was largely Christian. Note, the Peshmerga there refuses to arm the Christians.
In Shingal Mountains not high Muslim content. The Iraq Peshmerga don’t want the Ezidi’s armed. They would kill them all if allowed. We don’t appear to understand that.
In N Syria it depends on the community, but a fairly large Christian and Zorasterian content. They also leave atheists alone. And the numbers are increasing in both groups. Rojava is under sectarian rules there now. Syria in general, until ISIS, were not as oppressive to Christians, especially in the Kurdish area even before the war.
Basically what in the end saved Europe was a civil war within the ranks of Islam, centuries ago. Win win when they fight each other.