Thanks for the link to that interesting essay. It seems to rely on the possibility of inter-subjective truths (i.e. truths that should persuade) that are not objective (i.e. based on empirical results). Basically, I don't believe in inter-subjective truths of that kind because they are capable of proving too much. For example, "God exists" is a plausible candidate for inter-subjective truth, but there are empirical things I would expect in a world where God exists that do not appear to be present. In short, there seems to be no limit to what can be labeled inter-subjective, non-objective truth.

Most small deviations, and practically all "radical" deviations [in cultural beliefs], result in the equivalent of death for the organism: a mass breakdown of civilization which can include genocide, mass poverty, starvation, plagues, and, perhaps most commonly and importantly, highly unsatisying, painful, or self-destructive individual life choices.

This asserted fragility of society is inconsistent with historical evidence. You can pick just about any moral taboo (E.g. human sacrifice or incest) and find a society that violated it but continued on, and fell for reasons independent of the violation of the moral taboo. For example, Nazi Germany didn't lose WWII because they were immoral jerkwads. Germany lost WWII because it picked a fight with a more powerful opponent (who happened to also be an immoral jerkwad).