The correct answer is D) Islam.
The religion that became the strongest rival of Christianity in the Mediterranean area during the time of the Byzantine Empire was Islam.
Islam spread basically bu conquest, trade, and evangelization during the Byzantine Empire times. The Byzantine Empire was the Eastern part of the Roman Empire that lasted another 1000 years after the fallen of the western Roman Empire. Traders and conquerors took Islam from the Arabian peninsula to North Africa, the Middle East as far as the Iberian Peninsula. The Ottoman Turks, who were Muslims, spread Islam in the Byzantine Empire.