Context time! The manga doesn't explain this, but the act of the monks carrying Mikoshi into the city while rioting is basically weaponising their religion.
The Mikoshi are portable shrines that are said to house the deity/deities. Today we see them being used in processions to transport the god from one shrine to another or for sacred festivals.
Imagine you're charged with the security of the city, you're damned if you let the monks riot. It'll get bloody if you allow the confrontation to escalate to a melee cause the warrior monks are badass.
You're also damned if you fire arrows wildly into the crowd of protesters because you'll hit the mikoshi, basically committing blasphemy against the Gods.
Ultimately, you can't control your soldiers. It takes just one frightened guy with a bow to fire into the crowd, to start a volley, killing monks and covering the mikoshi with arrows. The monks will use that as another excuse to continue their rioting because the lord of in charge is clearly a heretic.
Worse, everyone else who wasn't killed under those circumstances will also blame the lord because disrespecting the Gods will likely call down disaster upon the country.
Nobunaga actually isn't the first warlord to engage the monks in military conflict, he's just made infamous for it because he had many other detractors who had other bones to pick with him and used it as an excuse.