I don't think Entropy has a unique identity right now, and I think you demonstrated that by saying it's easier to define what Entropy isn't, than what it is. If the Immortals running the cabal can't define what the cabal is about in simple terms, how can you expect a player-run character to live those ideals?

It's pretty easy to define every other cabal in very simple terms:
- Fort wants to protect good people and kill evil people.
- Empire wants to impose their rule over everyone and consolidate power for themselves.
- Outlander wants to destroy civilization.*
- Battle wants to end all mortal use of magic.
- Scarab wants people to be their true selves, without hiding behind false morality.

So, how do we finish this sentence: "Entropy wants to..."

If I'm not mistaken, they have two real goals:
1. End civilization.*
2. Ensure magic is free and unrestricted.

Two problems though:
Entropy's first priority seems to mirror that of Outlander. Why do we need a second organization that wants to destroy civilization?
Entropy's second priority is hypocritical. They want magic to be free, except they don't like binding magic. So all magic but that kind should be unrestricted? Seems like they are creating artificial barriers on the practice of magic, yet still fighting against OTHER artificial barriers.

I get that they're all about freedom, but freedom to do what you want (except things we don't like) is an ideal that's already taken by Outlander (and, arguably, by Scarab). It's just a slightly different take on what's already available.. and outside of a necromancer (who could likely find a home in Scarab), I doubt there are many Entropy-specific roles that wouldn't also work in Outlander. It's a niche cabal, except without a niche.

My recommendation would be to remove that first priority (ie, ending civilization), and double down on the whole magic thing. Make them about freely practicing and researching all forms of magic, and actively destroying all barriers to that (ie, cabals that would hunt them). That would make the cabal still interesting but with more clearly-defined goals, and also place it smack in the middle of cabalwars, rather than far on the outskirts.