I wouldn't be terribly opposed to a lord of altruism or comradery,

You fundamentally misunderstand the Tau. They're not altruistic, they're just the least-worst civilization. They're closer to a space Roman Empire than they are to communism. They'll conquer you, put you in a pseudo-slave caste, and collect taxes. They can only claim to be a lesser evil because every other civilization's default response is genocide.

What kind of chaos god would they make?

Probably something to do with absolute control. The Greater Good is an authoritarian philosophy in which individual citizens don't really have any rights. They have certain cultural freedoms of course, but no right to self-determination. For warp-sensitive races that believe in this philosophy, it would show up as a desire to dissolve the ego into the whole. This could create a god which seeks to create a galaxy wide hive-mind of sorts. A sort of warp based Tyranid empire composed of multiple races which would subject entire planets to experimentation for the greater good.