As is quite typical in this sort of thread, this isn't too hard, but the end product won't look anything like OTL Judaism and almost certainly won't be called that either.
It's not clear how monotheistic the Hebrews would actually have been when they first encountered the Phoenicians, or whether they would simply have been raising one Canaanite god (El) among all the others. So in theory, having the Phoenicians also start increasingly venerating El above all other gods should be pretty simple (though they did tend to prefer Hadad, but the Jewish god has aspects of both, so...)
The problem is that Judaism - or perhaps a better named would be Hebrewish or Israelism at this point - as a religion was very closely tied in with a small, agricultural, highly centralized state centered on the region between the Jordan and the Sea. The Bible includes large tracts on land allotments and how to farm. The Jubilee in theory prevents the accumulation of too much wealth in any single family's hands as property is supposed to revert to its "Biblically ordained" owners every 50 years (yes, there are easy ways around this, but the idea is there). There are holidays that require everyone make annual pilgrimage to Jerusalem, there is an ordained priest caste funded by tithes...
While I have absolutely no doubt that the Phoenicians could adopt something that both they and the Hebrews initially agree is the same religion, and that the Hebrews would probably tend to follow the Phoenicians' lead if they become rich and powerful, it seems to me that either the religion will be about as Jewish as modern Christianity, or that the Phoenicians would be too shackled by it to be the OTL sailors, traders, and colonizers that we know and love.
And it probably wouldn't be called "Judaism", as that name gets during the Hellenic period.
Roughly this.
Of course, there is room to believe that early Judaism started out as one of many local variations of a Canaanite religious, cultural and linguistic continuum which did actually include the "Phoenicians" (who actually called themselves Canaanites,or Tyrians, or Sidonians; "Phoenician" is a Greek exonym, possibly derived from an Egyptian word; but in any case, the peoples that the modern Western historical tradition singles out as "Phoenicians" appear to display little if any awareness of such shared identity).
It could be said, with some exaggeration, that Judaism is the only surviving form (highly transformed) of the general Canaanite religious tradition that existed in the middle Iron Age.
Of course, that tradition as it is testified by the Old Testament is actually a synthesis from a slightly later period, although it incorporates a lot of texts, beliefs and practices that go many centuries earlier.
I would say that Phoenicia was "Jewish" (better to say the reverse: Judea was "Phoenician") up the Assyrian conquest, in the sense that the cultural practices and traditions, including the general outline of religious life, was pretty much similar in Tyre and Jerusalem; while the Phoenician societies never developed actual monotheism, they the same fertile ground to do that manifested in Jerusalem.
Actual monotheism appears to have consolidated in Judaea roughly during the Assyrian-Chaldaean interregnum, and further established during the Babylonian Exile in which, unlike other Canaanite groups, Jews managed (were allowed to) preserve most of their cultural practices related to cult and, critically, their ethnic identity (in relation to said practices).
There are, as Minchandre correctly notes, some critical differences in the economy of the coastal and interior/hill Canaanites; but had the Tyrian scribal and priestly elite been able to preserve the ethnic, cultual and political cohesion and continuity (of sorts) that the Jerusalem elite managed to have, you could possibly have a "Baalite" monotheistic, or at least monolatric, religion (not guaranteed of course, but again, the basics were probbaly there).