Yes, but that religion was heavily influenced by Roman culture in a way Islam was not. All the above mentioned countries still live virtually entirely under the

Yes, but that religion was heavily influenced by Roman culture in a way Islam was not. All the above mentioned countries still live virtually entirely under the morality and worldview shaped by that religion. Christianty is a religion heavily influenced by the Roman civilization, Islam is not. The nations mentioned all still abide by the beliefs inherited from the Roman past to a much greater extent than the Islamic nations. The Catholic Church specifically (which was the only church until the reformation) was and is a Roman institution. The groups that splintered off in the reformation were still heavily shaped by the 1000+ years of of this dominance. That is why they (and all other Christian nations) can to at least some extent claim to be descendants of Rome in a way Islamic nations cannot. Just because there are competing claims does not make all claims equal. Islam being the dominant belief system precludes a nation from being an heir to Rome in any meaningful sense.