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?
I posted a link to a very informed and detailed article some 2 months ago on FR. I need to look for it. But here is another related one and other links within it about ISIS (Daesh) and its economy — http://edition.cnn.com/2014/08/18/business/al-khatteeb-isis-oil-iraq/
“I have read they are communalists.”
I was speaking about the Kurds, not ISIS.