Well that's not true at all. Early Christianity spread so well across Europe and the Middle East before the collapse of the Western Roman Empire because it happily syncretized with existing polytheisms. Unlike Buddhism, which largely did not displace those polytheisms, early Christianity syncretized those religions out of existence by adopting core theological concepts (e.x. the idea that God could Incarnate into a human person), coopting major holidays (e.x. Saturnalia became Christmas), and recasting divine or semidivine figures as Christian saints or angels (e.x. St. Brigid). (See this paper for an explanation.)The question as posed doesn't work.
Christianity and Islam are very, very weird among world religions in that they really resist syncretizing influences and tend to spread like wildfire. Judaism and Zoroastrianism were extremely resistant to syncretism, and Buddhism was proselytizing, but Christianity was the first faith which was really well suited to be both. Without it there's very little chance that you have a single religion come to dominate the region.
I disagree. A unifying theology or philosophy across an area as vast as China or the Mediterranean requires a unifying state or statelike entity to enforce it. China maintained continuity because institutional hegemony was recurrent and cyclical. Consider the unification of the numerous Dharmic religious sects into a singular Hinduism, which only occurred in reaction to both the Mughals and the British. The Mediterranean world was only dominated by one empire just the once! OTL the Catholic West and the ERE weren't even able to maintain philosophical unity, and they nominally shared a religion!The likely outcome is that the Middle East and Mediterranean world come to look a lot like China. What I mean by this is that Neo-Platonism, Stocism and other Hellenic philosophies occupy central role (like Buddhism and Confucianism) while most people follow folk cults and worship an array of gods depending on their heritage and needs. Likely something similar to OTL Gnosticism spawns out of Platonism even without Christianity, it may become the dominant belief. But without Christianity our very defintion of religion is going to change from an exclusive categorization to something that is unique to literally every individual.
Absent Christianity, Judaism would remain dominant in the Levant and eventually be the majority across the Mashriq. OTL is was relatively widespread, with Jewish kingdoms across north Africa and Arabia as late as the Islamic conquests. It, alongside Zoroastrianism, Buddhism, Neoplatonism, and other religious theologies would continue to persist throughout the Mediterranean, whereby different groups in a post-Roman world would adopt one or more of them as unifying philosophy.