I find that claim to be very implausible: to name just one objection to it, it seems to assume that morality is essentially "logical" and based on rational thought, whereas in practice moral beliefs seem to be much more strongly derived from what the people around us believe in. And in general, the hypothesis that all moral beliefs will eventually converge seems to be picking out a very narrow region in the space of possible outcomes, whereas "beliefs will diverge" contains a much broader space. Do you personally believe in that claim?
That argument seems like it would apply equally well to non-moral beliefs.
This is a thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. The previous thread is at close to 500 comments.