But your observances only reflect much later stages of Christianity, many hundreds of years after the time of Christ, when it had become a deeply politicized. And just because the old pagans were conquered by Christian emperors, which they had to be as they became criminally inclined predators and pirates, doesn't mean that their conquest was due to any edict by Christ to spread Christianity by the sword, as in the case of Islam.
In its earliest and purest form, Christianity was not in the least politicized and wasn't spread by the sword, it's spread being more like Buddhism than Islam. Moreover Christ's coming is attested by numerous prophecies in the Old Testament and the whole plan of salvation mapped out in advance, before he ever set foot on earth. Not so for Mahomet, who suddenly appeared with no prophecies relating to him of Islam except as appear in Revelation Chp. 9, where of Mahomet it is said "They had as king over them the angel of the Abyss, whose name in Hebrew is Abaddon and in Greek is Apollyon (that is, Destroyer)."
So bereft was Islam of any attestation for Mahomet that the Koran even plagiarized Christian documents in a curious mistranslated way, which accounts for the 70 virgins in heaven and other such fantasies.
For that is what the Caliphs were: destroyers of ancient civilizations: for the most part Persian and corrupted Christian.
There were some forced conversions it is true, especially from monotheistic Jews to a corrupted (in their eyes) Trinitarian form of Christianity, but in general most pagans willingly converted on account of their recognition of their old gods as worthless. With the Jews the problem has always been the irreconcilability of the Greek additions to Christianity with strict Jewish monotheism. For the Jews had always accepted in principle the idea of a Messiah, as it is written into their own scriptures.