Ignoring the theological argument that took over the last four pages, when developing this TL, you should keep in mind our historical relativism.
The Judeans/Israelites were a tiny tribe in a world where there were hundreds of tribes. I have to agree with the posters who say there were MANY groups that could be defined as Monotheistic. However, that world is itself an invention by a culture that is primarily Monostheistic. Hinduism (go speak with a Hindu yogi, I attended a teaching by
Swami Mukundananda) can be defined as Monotheistic, Polytheistic, or Pantheistic, depending on where you are in your spiritual journey. That's exactly what makes it such a stable religion: it allows different paths to the Brahman.
With that in mind, you can take ANY of the tribes that existed (for arguments sake, we'll use the Hellenics) and just watch as the lesser gods fall to the side and the primary god is worshipped above all else. For example, say Alexander's empire stays together. The Hellenics could promote their religion, but adopt other pagan deities as wives, sons, or brothers of Zeus. Theory goes that YHWH followed a similar path, as a war god among many, who became primary above the other Israelite gods as the Israelites conquered more and gave more credibility to their war god. Pros: You get your monotheistic religion that allows homosexuality as surely known homosexual Alexander III would be a prophet of Zeusism. Cons: Zeusism would just be the biggest butterfly in the swarm resulting from a surviving Alexandrian Empire.
I'm actually surprised this thread is so focused on Monotheism. In the timeline I'm working on (but haven't released), the biggest religions are Buddhism and Shintoism. Buddhism, spreads to the Near East rather than the Far East and spreads via trade from Europe* to India/China. Shinto spreads as Japan becomes the primary colonizer of the New World. I love Shintoism because it's so much more than a simple polytheistic belief. The Kami of Shintoism, as in Hinduism, can be worshiped as anything from many individual and simple spirits, to full a full embodying reality. It all depends on the worshiper.
That's my 2cents: when it comes to religious PODs. It's easy to get caught up in our own definitions of religion and religious philosophy, especially when we don't belong to that religion (I'm looking at you, non-Zoroastrians, non-Hindus, and non-Native Americans), but try considering religious history from the point of view of the worshiper.
(On that matter,
here's an interesting OTL from the Hindu POV)