Islam is a contested, multi-faceted field just as Christianity, Judaism, and other religions are. The Baathists were secular, but at the same time, they also incorporated Islam into the legitimation of the regime. It is a bit ironic for the Assad regime, which is Alawite, to incorporate Sunni Islam into the regime, but they actually did. They gave it official state status as the main religion in the country. Of course, Saddam, in his later years, added the Allahu Akbar to the Iraqi flag in his handwriting, and more and more justified his rule under Islamic discourse. That has only become a more pronounced tendency among many groups since 2003, and of course since the outbreak of the Syrian civil war, communities like the Yazidis, the Christians, and the secular Kurdish groups want nothing to do with that. There are also Kurdish Islamist groups, but they're minor.
In a power-sharing or decentralized system, when Baghdad, say, passes a law banning alcohol or banning women from wearing skirts or trousers, it doesn't apply to other regions where the consensus is that this is not what they want. A way to defuse some of those divisions and contests over the nature of Islam and whether it should be enforced is to have more decentralization. That said, we have a violent Salafi bent out there that has still not given up on enforcing its interpretation and imposing it on everyone else.
It's going to ebb and flow whether or not people primarily identify according to religious discourse, ethnicity, or tribe, but we know that the more insecure people are, the more likely they are to fall back on one of these identity categories as their primary one, as opposed to a regional or civic national identity that requires more trust of out-group members.
I don't know if I answered your question at all.