> What confuses me most about Israel’s rising political turmoil is that the faction driving for violence against Muslims (the ultra orthodox) are also exempt from the military.

That's mostly inaccurate. Most Haredi people don't "promote" any violence against Palestinians, since they don't see themselves as part of this conflict (they mostly identify as non Zionist), don't go to the army, and in general don't participate in any violence against Palestinians. You might be talking about religious zionists, most of their men actually do go to the army.