When I used the term Leftist it may have been a poor choice of words.
I have read they are communalists. If there is such a word.
ie they are not capitalist in nature.
In that part of the world who knows what really makes sense.
Capitalism is an economic stance, not a religious stance, as you know.
In fact Saudis, their satellites, Qatar and other Gulf Sheikhdoms are all 'capitalists' in an economic sense. They run their trade business akin to Corporations.
Actually, Daesh (ISIS) is too. So far, Daesh (ISIS) actually runs its own Ministry of Finance & rules over a couple of million at least, currently in Iraq & Syria combined. In their wheelings and dealings, they are extremely "Capitalist" ie their economy.
Politically, however, their ideology is hardcore Sunni/Salafist Islam; that makes them very much right-wing, in their Islamic political ideology. Nothing else is tolerated at all. No minorities, no Christians, no Jews, no Zoroastrians, no Yezidis, no Ba'hais; nothing else.
Does what I said make sense?