It was a blessing for a defensive war. Serbians didn't "go" anywhere to attack Austrians. It was the other way around. But I guess you already know that. Why did you choose to write "to go kill" when they didn't go anywhere?
Sure, after the declaration of war by the state. The Church (depending on which definition you use) sponsored plenty of Crusades too. None of these actions are ‘rebel against the machine’.
Though that does sometimes happen, usually leading to/in the middle of a civil war.
https://images.app.goo.gl/dqHBEnQvy2hc6RHD8
This is them blessing the troops to go kill the Austrians a month later.