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Nate_Gabriel comments on Anthropics doesn't explain why the Cold War stayed Cold - Less Wrong
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I still don't think George VI having more siblings is an observer-killing event.
I assume you mean "know" the usual way. Not hundred percent certainty, just that I saw it on Wikipedia and now it's a fact I'm aware of. Then P(I exist with this mind state | George VI had more than five siblings) isn't zero, it's some number based on my prior for Wikipedia being wrong.
So my mind state is more likely in a five-sibling world than a six-sibling one, but using it as anthropic evidence would just be double-counting whatever evidence left me with that mind state in the first place.
Yep; in which case the anthropic evidence isn't doing any useful explanatory work, and the thesis 'Anthropics doesn't explain X' holds.
Anthropics fails to explain King George because it's double-counting the evidence. The same does not apply to any extinction event, where you have not already conditioned on "I wouldn't exist otherwise."
If it's a non-extinction nuclear exchange, where population would be significantly smaller but nonzero, I'm not confident enough in my understanding of anthropics to have an opinion.