What you call “persecution” was the needed correcting of heresy and the promotion of “orthodox” or right Christian faith. There were a LOT of heresy at the time.
Three centuries of slaughter of Donatists, Montanists, Arians and others, along with east-west controversies where those groups mixed, mainly in north Africa caused Christians there to welcome the Muslim invaders who were neutral on these schisms but stopped the “Christian” on “Christian” bloodshed. And it was mainly the orthodox of the east and west doing the killing with support of the Roman/Byzantine state.
No true Christianity is spread by the sword.