In MM the Yugoloths are described as having only one question in their mind: "whats in it for me". They are Neutral Evil.
Alignment is a part of any character design with depth, whether you use two words or 500 words to describe it. Removing an arbitrary system of binomials and acronyms from the game doesn't magically eliminate the concepts of law and evil. Alignment or no alignment, players of "good" characters are going to try to get away with crap they shouldn't get away with and dungeon masters are going to have to take them to task for it. That's our job. The only thing that changes with the removal of alignment mechanics is that a few clumsy tools have been removed from our arsenal.
Spoiler: It's not going to save the players.
Of course that is also a completely legitimate optionThis is a great example of the opinion I don't understand. Why is Chaotic Neutral the one alignment that is exempt from holding true views? I acknowledge that this is personal perspective, but if I were playing a devoted Chaotic Neutral character I would leave all four churches intact and work to increase the discontent the imbalance must cause. Now, if any of them were /lawful/ churches, /those/ would get the torch -- the same way a devoted Lawful Neutral character would do everything in his power within the law to get a chaotic church closed, its members arrested, and the religion banned from the city.
I must confess though, some of the things you're saying kind of worry me... from what you say, it sounds like you don't really trust your players to play their characters correctly and rely on the alignment system as a way to fight them. You really shouldn't have to weaponize rules just to keep players in line. Is this typical of games you run? If so, perhaps you should try to clear the air with your group and see if you can improve the overall playing environment? You'll probably have more fun with the players if you only fight them through the monsters. I don't want to impose or anything, though. It just seems like there might be something keeping you from getting full enjoyment out of the game. I want people to enjoy it as much as they can! :>
But see what's happening here? This is what the alignment system does to people! By assigning specific labels to nine distinct philosophies, it just encourages people to argue over how to define each label correctly! If there wasn't an official in-game classification for these viewpoints, the only people who'd be arguing would be people who really liked identifying the philosophical beliefs of fictional characters.