Filtering different types of FB notifications is really a problem that needs to be solved in their app, not in Android.
It's a team effort, I'd say, though facebook is where I lay most of the blame. I'm just ranting in general about the state of notifications and how insistent and entitled so many apps have become on many platforms, not really calling out specific operating systems or developers (though all the notifications I was complaining about in Windows were from Windows itself and not facebook or the like, so we have to lay all the blame on Microsoft in that case).
Edit: after thinking about it, I don't think the OS should impose good taste (eg to prevent Facebook messenger head bubbles from being really annoying and obstructing other apps), since that would mean apps that legitimately need that ability wouldn't be able to do so. I'd guess Twilight, a blue screen filter app I use and like, wouldn't be able to do it's thing if Android didn't allow apps to operate on other apps display. Facebook just needs to stop being so obnoxious.
So, the apps I don't absolutely need to hear from get disabled completely, even though there are notifications I would welcome from those apps. facebook is perhaps the most annoying because I know they have the ability in-house to get this right. They're choosing not to, and they're choosing to ramp up the user-hostile behavior, because having people constantly engaged with facebook is profitable.