I don't really see every cabal as having a "direct opposite". This is my view of it:

Fortress vs. any evil, regardless of cabal or uncaballed.

Empire vs. everyone.

Scion vs. everyone.

Battle vs. Scion, Nexus, and any magic regardless of cabal.

Tribunal vs. Outlander and Wanted

Outlander vs. Tribunal, Empire, Scion, and I think Fortress should be part of that list for any non-good Outlander and some good.

Herald vs. Tea and Cake

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Granted, may not work out in practice, but that is how my characters would see it if they were in any of the cabals.