This is a common misconception. The Edict of Milan was granted by Emperor Constantine in the West and Licinius Augustus in the East in 313 granting religious freedom throughout the Roman Empire. In addition, the Edict of Milan ordered the restitution of property confiscated from Christians.
Christianity had to wait many years later under a different emperor to become the official religion of the empire.
Regardless, there were lots of Christians and Jews living in Mecca when Mo was born.