…He would be an idolater.
Think about it- God is jealous to protect His honor, His glory. God’s jealously is righteous because He wants to be recognized for who He is.
Some Biblical support:
Exodus 20:5 “You shall not bow down to them or serve them, for I the Lord your God am a jealous God, visiting the iniquity of the fathers on the children to the third and the fourth generation of those who hate me”
Exodus 34:14 “(for you shall worship no other god, for the Lord, whose name is Jealous, is a jealous God)”
Deuteronomy 4:24 “For the Lord your God is a consuming fire, a jealous God.”
Deuteronomy 5:9 “You shall not bow down to them or serve them; for I the Lord your God am a jealous God, visiting the iniquity of the fathers on the children to the third and fourth generation of those who hate me,”
Isaiah 48:11 “For my own sake, for my own sake, I do it, for how should my name be profaned? My glory I will not give to another.”
(I included Exodus 20:5 and Deuteronomy 5:9 because when God repeats something in Scripture, He means business)
God alone is deserving of all honor and glory. God is right to view Himself as the One of ultimate value. If He were not jealous about protecting this, it would mean that He sees something else as more important than Himself.
If that were the case, God be an idolater.