C'est magnifique.
What I am imagining: Something to keep us occupied into the late game - a new way of causing !!!FUN!!! if you will.
On the one side - less fervent believers, the philosophical dwarves.
On the other side - more fervent believers, the religious dwarves.
Each listens to their Philosopher/Priest, shares, converts, fights, kills and dies for their cause. Every dwarf can belong to both, and each School of Thought or Religion can become dominant (and compatible ones (e.g. a warlike philosophy with a murderdeathvonkillingham god) can be dominant simultaneously. When fighting breaks out, loyalty resolves based on what's more important.
To give an idea of how complex (read: awesome) this could be, let's take some SIMPLE examples
Urist McMarxist
Religious Proclivities: Modest
Philosophical Proclitivities: Starting revolutions for Fun and Profit by Urist McMarxist
Religion: Murder (advocates killing of sentient beings, conquest, etc.)
Philosophy: Commie!
Urist McHippie
Religious Proclivities: Strong
Philsophical Proclivities: Moderate
Religion: Rainbows
Philosophy: Communism.
Urist McBornAgain
Religious Proclivities: DOWN WITH ALL HEATHENS
Philosophical Proclivities: Does Not Think For Himself
Religion: Volcanoes
Philosophy: Capitalism.
So, a religious conflict breaks out between the god of murder and the god of volcanoes (against all odds), obviously McMarxist and McBornAgain are on opposite sides of the battlefield, but where will McHippie go? He'll support his communist brethren in the religious war even though it goes against his own beliefs for the sake of some advantage.
When multiple conflicts start happening, their preference for Religion or Philosophy will determine which side they will stick to, to avoid an unending loyalty cascade, such as the possibility of being compelled to assault yourself from your other side. (e.g. the first one will support his communist ideals over his murdergod, while the latter two will go with their gods rather than their philosophies, whenever these have conflicting purposes)
Imagine, if you will, a tantrum spiral that serves a purpose.