From the standpoint of Jewish tradition, which accepts that the Pentateuch was transmitted to Moses in its entirety around 3,300 years ago, it is clear that the Jewish religion was always monotheistic rather than monolatristic. See Deuteronomy (4:35):
Unto thee it was shown, that thou mightest know that the LORD, He is God; there is none else beside Him.
Know this day, and lay it to thy heart, that the LORD, He is God in heaven above and upon the earth beneath; there is none else.
Also note Isaiah (44:6):
I am the First and I am the Last, and besides me there are no gods.
Similar examples include II Samuel (7:22), Isaiah (45:5, 45:21-22, 46:9), Psalms (86:10), and I Chronicles (17:20).
In the context of the above verses, it is evident that passages referring to other deities do not imply that the Bible recognizes that they exist in the same sense that devotees of those religions believe, but rather that they exist within the beliefs and mythologies of those religions.
There were periods when many Jews abandoned Judaism to worship other deities (sometimes without totally rejecting traditional Jewish worship, see for example Kings I, 18:21), and there were probably other individuals who exhibited monolatristic beliefs, but this was a departure from the normative Judaism of the Bible.