Knowing a couple people who work at Anthropic or in their particular flavour of AI Safety, I think you would be surprised how sincere they are about existential AI risk. Many safety researchers funnel into the company, and the Amodei's are linked to Effective Altruism, which also exhibits a strong (and as far as I can tell, sincere) concern about existential AI risk. I personally disagree with their risk analysis, but I don't doubt that these people are serious.