It seems that even IOTL Rome was pretty close to Monotheism early in its Repuplican history. Here are some parallels between Jerusalem and early Republican Rome:
- The Capitoline Jupiter Temple is said to have been built after a wholsale removal of a large number of shrines and altars deedicated to various Gods: similar to Josias campaign to remove shrines "on every high hill and under every green tree"
- A temple to a warlike feminine deity at the foot of the Capitol (the Sant'Omobono site) seems to have been put to the torch and pulled down just prior to the building of the Capitoline Temple: similar to Monotheistic Judaism fight against Astarte worship.
- The senatorial class originally held a monopoly on priesthood and it was the source of its subsequent political power: the Sanhedrin and the Zadokite priesthood families.
- Romans are said, in classical times, to be "the most religious of peoples".
All of those parallels are either misleading or far too general to be of use. There were supposedly a lot of shrines on the site that would later be occupied by the Temple of Capitoline Jove, but there's no historical evidence to suggest that the building of the temple was intended to denigrate these other deities, and the archaeological record indicates that major temples were built for a variety of gods during the same period. The Sant'Omobono temple was more likely destroyed due to associations with the Roman monarchy than as part of any anti-monotheism programme. And I hardly need to point out that "having a politically influential priestly class" and "being religious" could be predicated of many societies throughout history, including indisputably polytheistic ones (e.g., Egypt).