Chaos Marxism stands for separation of church and state; and of the personal and the political. Not in the sense that they have nothing to do with one another - on the contrary, there's a strong dialectical interrelationship between the social microcosm and the social macrocosm, because that's what we're talking about on this blog. But don't confuse the levels.
Frank Zappa said "You can't run a country by a book of religion". Well, it might be objected that the early Islamic ummah did reasonably well for a few centuries, but that wasn't being run entirely on the basis of the Noble Qu'ran, but on the personal authority and example of the Prophet, peace be upon him and all that. That gave the system an essential flexibility and humanity that is lacking from all dogmatic structures - and from arbitrary personality cults, at the other extreme. There are good forms of religious-inspired political activism which realise this, and bad forms that just want to show a particular legalistic interpretation of the Bible or the Qu'ran or the Collected Works of V. I. Lenin or Quotations from Chairman Mao down your throat. That crap will last a few decades and collapse, at best. (Unless, sadly, it's sitting on a buttload of natural resources. We need to understand exactly what the House of Saud have been up to for the last few decades - simultaneously schmoozing with the worst scumbags among Western capitalists, and spreading an interpretation of Islam which is pretty much all sword and no heart on a global scale.)
At the other end of the scale of trying to use your personal religious beliefs or identity as a means for social organisation or activism, of course, lies the trap of using your political activism as a substitute religion or identity. This is of course what we've been cursing out on this blog for ages - the essential solipsism of sitting at home polishing your soul while the world falls down outside, while engaging in "play-politics" to make yourself feel better. One way lies heartlessness - the other, uselessness. Marx and Lenin never gave any indications for how you should live your life, nor should they have. Find one that works for you and is consistent with the principles of the new world they wanted to build.
The poet Rumi said: "Faith is one whereever you go, but beliefs are many", or words to that effect. So, a social movement which might have a chance of actually building a new world has to be completely firm on certain basic principles of action/communal effort, but completely tolerant on exactly how those principles might be expressed. The middle road - the best combination of the rational and irrational, personal mildness and firm principle, ends and means - is what any healthy and progressive social system needs. If you ask me, modern capitalism has gone all the damn way towards the irrational, which is why it breeds dogmatic cults such as fundamentalist Islam and Christianity as a counterbalance.
This is the principle of the united front applied to macrocosmic social organisation as well as to how we get on with our neighbours and friends. In Islamic terms, it is the fusion of the "greater jihad" of personal ethics and the "lesser jihad" of striving for social justice. From the Thelemic standpoint, we might distinguish the "lesser magick" of fighting back against the memetic bombardment of the current industrial deathculture and creating symbols and egregores that will serve us, and the "greater magick" of becoming the kind of people who will be fit of living in a new and better Aeon. The Prophet Muhammad and V. I. Lenin both got the job done because they knew how to make this combination, which is why they changed the world, each in their own way.