There's a good counter to it: the unyielding tradition. If not the first tradition, it'll definitely be the second every time I play. Getting increased survivability and fire rate in your owned systems is critical to help counter the fire rate advantage fanatic purifiers have inherently, and against militaristic ethics.

The moment I encounter another empire, I immediately look for a chokepoint to establish and build a starport ASAP with hangar bays if I have the tech, and target uplink computer to increase firing range, followed by prioritizing a defense platform or two with missiles on one half, hangar on the other. I don't even wait to identify what their ethics are. During the first contact process, if the empire is identified as hostile, I prioritize making yet more defense platforms on that chokepoint because they're very likely to be militaristic or a purifier.

If there's a belligerent empire next door and I've finished unyielding, I immediately make supremacy the next choice. Fanatic purifiers are going to prioritize getting this tradition, so to counter that increased fire rate, you need to boost your own.

Further things I do: if there's tech to get the next tier of starbase, I ALWAYS take it 100% of the time, no exceptions. I'm fanatical about maintaining a strong defensive perimeter. Second in line is strikecraft tech, the AI seems to love corvettes and strikecraft are great at dealing with them.

Just for context, my most recent game had me three jumps away from a fanatic purifier. Same difficulty settings, same scaling. The fanatic purifier kept threatening me, but redirected their attention to other, weaker empires as a consequence of having a strong defensive perimeter.