For each new visitor who comes in and accuses us of messianic groupthink how far should I update in the direction of believing them?

As long as the number is small, I wouldn't update at all, because I already expect slow trickle of those people on my current information, so seeing that expectation confirmed isn't new evidence. If LW achieved a Scientology-like place in popular opinion, though, I'd be worried.

Am I going to burn in counter factual hell for even asking?

No.