OK, I have not been able to eat enough today, so I'm a bit tired. I hope this will be coherent enough. I should note at the onset that I'm not an expert on the Byzantine Empire in this period, I have mainly read on it tangentially to the Sasanians or Islamic conquests.

So, we need to separate out Mesopotamia here, because this was the seat of the Sasanian court, wheras the rest of the Levant was under Byzantine dominion (the Sasanian occupation during the war notwithstanding).

The code of Justinian in the mid-6th century, while not directly outlawing paganism, certainly sought to discourage it and forbid certain practices. The Byzantine Empire at this point was a Christian state, with a Christian emperor. The very first paragraphs of the Codex state:

We desire that all peoples subject to Our benign Empire shall live under the same religion that the Divine Peter, the Apostle, gave to the Romans, and which the said religion declares was introduced by himself, and which it is well known that the Pontiff Damasus, and Peter, Bishop of Alexandria, a man of apostolic sanctity, embraced; that is to say, in accordance with the rules of apostolic discipline and the evangelical doctrine, we should believe that the Father, Son, and Holy Spirit constitute a single Deity, endowed with equal majesty, and united in the Holy Trinity.

(1) We order all those who follow this law to assume the name of Catholic Christians, and considering others as demented and insane, We order that they shall bear the infamy of heresy; and when the Divine vengeance which they merit has been appeased, they shall afterwards be punished in accordance with Our resentment, which we have acquired from the judgment of Heaven.

But bear in mind, this concerns Christian heresy. The point is made more clearly in laws concerning Jews and Pagans:

We grant permission to heretics or Jews, when they have litigation with one another, to introduce witnesses qualified to testify, with the exception, however, of those who are controlled by the Manichean insanity, which it is evident is also shared with the Borborites and those who believe in the Pagan superstition; and the Samaritans are also excepted, as well as those who are not unlike them, together with . the Montanists, the Tascodrogites, and the Ophytes, to whom all legal actions are forbidden on account of the similarity of their offences. We therefore order that the right to be a witness, along with all other lawful acts, shall be forbidden to the Manicheans, the Borborites, and the Pagans, as well as to the Samaritans, the Montanists, the Tascodrogites, and the Ophytes.

The bolded is particularly interesting - Manichaeism is, briefly put, a syncretism of Christianity, Zoroastrianism and Buddhism; Mani had belonged to a "Jewish" sect of some sort. Famously, St. Augustine was a Manichaean before his conversion. So it's pretty clear that the Byzantines accepted, however grudgingly, the fact that pagans and Jews resided in their territory; they only became an immediate threat if they showed tendency toward inciting Christian heresy.

Anyway, 100 years later, the Islamic conquests happened. I cannot recall having read anything that suggests that these regions were anything but generally Christian. That does not, of course, mean they practiced Christianity exactly as the Byzantines would have preferred them to. Islamic sources note, according to a neat little book called "Christians and Others in the Umayyad State", that Christian Arabs fought on all sides of the war. Heterodox groups, like so-called Nestorians, might have seen the invaders as an opportunity to assert independence from the theocratic Byzantine rule,

Therefore, while we can probably broadly say that most of the population was Christian, that should not necessarily suggest homogeneity in belief.

Mesopotamia is an interesting case. It is possible that Christianity was a majority religion there, it is possible that it was not. Christianity in Iraq dates back to the first century, and it has often been noted for the many syncretic and mystic movements that came out of it (the most famous being the aforementioned Manichaeism).

The Sasanians had a complex and varied relationship with religion. Zoroastrianism as they practiced it was an imperial religion, where Ohrmazd had granted the King of Kings absolute dominion. All, including the clergy, derived their authority from the King of Kings. To give an idea, though it is a much different era, in the 3rd century a powerful Zoroastrian cleric by the name of Kerdir came to power. He actually recorded several length inscriptions; one notes:

And Jews, Sramans (Buddhists), (10) Brahmins, Nasoreans (Orthodox Christians), (Gnostic) Christians, Maktak (Baptisers), and Zandiks (Manichaeans) in the empire were smitten, and there was destruction of idols and scattering of the stores of the devs and god-seats and nests was abandoned.

As you can see, even this early they seem to have at least three distinct words for Christians. Armenia and Georgia, in the vicinity, would come under the Suzerainty of the Sasanians in the 5th century; though historically Zoroastrian, they had at this point adopted Christianity, and Christian sources are in general of major importance in studying the Empire. There was also a large urban Jewish community since the 6th century BC, which remained a large portion of Baghdad's population until the mid-20th century.

Therefore, while we do not have the data to absolutely assert majority everywhere, Christians formed a substantial part of the population throughout the Mashriq.

Apart from the aforementioned Christians and Others in the Umayyad state, I relied on (my memory of) Hoyland's In God's Path, and the chapters on Manichaeans and Christians in "The Wiley-Blackwell Companion to Zoroastrianism"; finally also "A State of Mixture" by Payne, on Christians in the Sasanian realms.

Hi! Just for clarity since the term has many meanings historically: by Levant, do you mean the Mashriq? Do you include Mesopotamia (Iraq) or not? This will be important for my answer.