Depends on what part of the Middle East you are talking about but there wasnt a "dominant" religion really unless you are very specific on the region. It wasnt Judaism in most parts of the middle east, it was split between Zoroastrianism and a lot of different pagan religions like the Graeco-Roman paganism, the Arab pagan religion etc. There was Judaism in many places like in the Arabian peninsula but I am pretty sure Zoroastrianism and Graeco-Roman paganism were the most common. That being said during late antiquity a lot of people worshiped multiple gods from totally different mythologies like Isis and Cyrene. Also for a lot of the pagan religions a lot of other minor sects would break off or be different enough to be considered a different religion. Like Aion was kind of like a very brief monotheistic religion based around Greek mythology.

Your question has to be more specific because the modern word and definition of "middle east" accompanies a huge area.

The "Middle East" is a very large swath of land. I presume you're asking specifically about the Arabian peninsula and Mesopotamia which I'll get to, but if we take it to mean the area between and including modern Egypt and Turkey East to Iran, then we can reasonably narrow it down to three "spheres": The Roman Empire in the West including most of Turkey, Egypt and the Levant; the Parthian Empire in the East including most of Mesopotamia and Iran; and the Arabian Peninsula in between.

The two empires are largely well documented, the Roman Empire most thoroughly. Obviously there was the Imperial Cult which predominated, as well as Judaism primarily in the Levant. There were also somewhat localized (or at least relatively uncommon) cults as well, including the cult of Isis in Egypt and Cybele (who would be absorbed into the Imperial Cult). Mithraism was also paritcularly important, though I'm not sure how widespread it actually was on the eve of 2 AD. Due to the effects of Hellenization after Alexander's conquest and the Diadochi, the Hellenic pantheon had an established foothold, but was not universal. There are many, many sources you could look to for Roman religion at this time period, but if you'd like some, just ask.

The Parthian Empire is a bit more complex because there was no enforced state religion. The three primary faiths in no paritcular order were Zoroastrianism, the Babylonian Pantheon, and the Hellenic Pantheon as a result of the Seleucids. There's a traditional belief that Zoroastrianism was the religion of the nobility, which is under some debate as to how true that really was for different periods. In any event, there were many Zoroastrians in the Parthian Empire, particularly in Armenia. The Babylonian religion continued in force through the Seleucid period and into the Parthian period, and the Hellenic religion was still a major force as well. A good source on this is Sasanian Persia: The Rise and Fall of an Empire by Touraj Daryaee. It's focused a bit later than 1 AD, but with the background information it still holds in my opinion.

As for the intermediate area in between and South of the two empires, that's where things get really hard to pin down. First, a note about Arabian geography: There are two lesser cultural "regions": Mesopotamia, and the Arabian peninsula. The peninsula itself is known in Arabic as al-jazīra al-ʿarabiyya, or the Arabian island. It's bordered on three sides by water, and on the final side by deserts that were notoriously difficult to traverse (so much so that people from one side frequently had to hire local guides to pass through to the other). We know a lot more about Mesopotamia than we do the interior of the peninsula, but there are things we can glean.

The Nabataeans lived in an area in the Southern Levant around Jordan down into the Peninsula proper. The Nabataean religion was based around pillar cults and sacred stones (Known as Betyls or Baetylus). It was polytheistic, and was influenced by both Hellenistic and peninsular cults. We see certain pre-Islamic deities represented in Nabataean sites, like al-'Uzza, who was a major deity throughout Arabia, and sometimes conflated with Roman Venus; Dushara who was conflated with Jupiter and found in the Mada'in Saleh ruins; and the husband and wife Hubal and Manat, and al-Lat (sometimes conflated with Minerva) of pre-Islamic Mecca. There were of course many other deities throughout the region. Constructing Nabataea by Bjö Anderson has some details about pillar cults and temples. There's also Arabia and the Arabs: From the Bronze Age to the Coming of Islam by Robert Hoyland.

I'd also like to take a moment to point out, from very early times there has been a cultural distinction between the settled agrarian peoples in the peninsula (focused around oases near the Hejaz mountains) and the Bedouin. The pre-Islamic Bedouin religion involves the same gods and goddesses (and some Bedouin made pilgrimage to the Kaaba during pre-islamic times along with other agrarian peoples) but they seem to have had a different approach to their religion than the settled peoples. There's an increased importance in shamanistic ritual and ancestor veneration instead of any sort of clergy. They did however, along with the settled agrarian peoples, have a particular focus on idols.

Judaism started to spread throughout the region during the Jewish-Roman wars and in particular after the sack of Jerusalem in 70 CE. The Himyarite Tub'a Abu Kariba As'ad, generally considered the first Arab king to convert to Judaism, only did so circa 400 CE.