Janice,

It's hard to argue against that question, given that is exactly what Exodus 34:14, Exodus 20:5, Deuteronomy 4:24, Nahum 1:2, and Joshua 24:19 say; not to mention Zephaniah 1:18 and 3:8, Zechariah 8:2, and Ezekiel 39:25. I need not go on.

• What's the exact objection under consideration?
• Would it help if I said that in a certain sense, this is an anthropomorphism?

It is speaking of God in human terms so that humans can understand the gravity of their sins. God is described in Scripture as the bridegroom, and His people as His Bride (see Isaiah 62:5, for just one example). God is trying to convey that just as a man would be jealous over his wife flirting with another man, so God is jealous over His people flirting with idolatry, in that He wants an exclusive relationship with Israel. So, He's communicating truth to them in ways they can understand and appreciate. 

The other gods are demons (Deuteronomy 32:17, Psalm 106:37, Baruch 4:7, 1 Corinthians 10:20, Revelation 9:20). They are our enemies and want to hurt human being as much as possible. They are extremely dangerous and worshipping them is definitely not in our best interests. The more we worship and obey them, the more we become like them, so God uses strong language to discourage us from doing so.

Janice,

I have a follow up comment. To give you an idea of what God was dealing with, one of the gods that God was constantly trying to pry the Israelites away from was Moloch (or Molech): See Leviticus 18:21.

The cult of Moloch is infamous for its brutal child sacrifice rituals, particularly noted in biblical and other historical sources. The sacrifices were a grim testament to the deity’s demand for appeasement through the offering of the worshippers' firstborn.

The practice was gruesomely vivid; parents would offer their young children to Moloch, hoping for favorable returns in their lives or for the community. The ritual involved a towering metal idol of Moloch, which was heated red-hot by a fire kindled within or beneath it. The children, once offered, were placed in the searing arms of the idol. As the metal scorched the children, their agonizing screams were drowned out by the beating of drums and other loud music, an appalling method intended to mask the horrific sounds of the execution and prevent the parents’ lament.

This brutal practice, centered around the power and appeasement of Moloch, starkly highlights the extreme lengths to which human sacrifice was embedded in the religious and cultural practices of some ancient societies. These rituals, reflecting a dark and desperate aspect of human belief systems, were particularly noted in regions around ancient Canaan and are repeatedly condemned in historical texts, illustrating the severity and inhumanity of such acts.

This is what God was "jealous" against.

Eric