This is a giant cheesecake fallacy. We could, in the future, create a society of beings which are identical down to the last bit. I, and I suspect most other people, would find such a society highly undesirable.

I reject the claim of committing a GCF. My statement was a reply to Unknown's claim that "no two physical things will ever be exactly alike.", which appeared in an argument that was specifically not restricted to humans, biological beings or intelligent entities. For this reply I was thinking more along the lines of "MNT assembler" than ">= human-level intelligence". If you build a technological infrastructure using small self-replicating machines, you probably don't want them to acquire random mutations without shutting down.