Why would Comstar want to fight the clans at this point? The best thing they could provide and Dark caste members is a route to the Inner Sphere so they could go become pirates proper, rather than live under the shadow of being hunted and executed by the ubermensch society.
Also not sure but, I doubt the society existed yet? Weren't they largely a sociological response to the shock of the Great Refusal?
ComStar doesn't really have a reason at this point, though of course that would change if they really understood the Clans (as they eventually did).
The Society has existed for more than a century, potentially going all the way back to the aftermath of Operation Klondike. Its genesis and core was always the geneticists-- also the most powerful and highest-status scientists. They largely agree with the Clan Way, except that they believe that their caste should be preeminent rather than the warriors. Keep in mind, many senior scientists are warrior test-downs-- so they have a chip on their shoulder to start with.
They'd been preparing a coup for decades, but were still nowhere near ready. The Bloody ilKhan's program of Reaving IS-tainted bloodlines was intended to break the power of the invading clans once and for all, but it terrified the geneticists who called most of the shots in the Society. They saw generations of eugenics going down the tubes and clan space going up in flames, so they decided to strike while they could.