No.
You can most certainly kill a guy shooting at you from a protected building, whether that be a mosque, hospital, etc. If you are going by a strict reading of international law, then those buildings lose their protected status the moment they are used for military purposes. Still, according to the same laws, you are obligated to minimize damage to those buildings. But you're getting into a grey area that's kinda unenforceable if you have legit combatants fighting from that position. Because at the end of the day, what is the appropriate use of force for X amount of guys using X ordinance?
Regardless, pretty much anytime we rolled into a new city (I was only there for the initial invasion and about six-months after) we took fire from pretty much three places: the mosque, the hospital, and the school. We shot back. No fucks were given.
As far as Blackwater goes, I never heard of them being used in any capacity other than general route clearing, security details (mostly in the green zone), and basic transport stuff. Granted, I never worked with them though, only interacted with them in garrison. Thought they were twats though.