The prepositions used are important. The text notes that worship in Israel included swearing to
the Lord while swearing by
Milcom, that is, by another god. By,
in this case, introduces the party that functions as a higher authority, and a guarantor of the oath being made. For example, in Exodus 32:13 the Lord swore to the patriarchs by himself.1 But that is a far cry from Zephaniah 1:5. Israel’s swearing by Milcom was a swearing by a false god, regarded as a divine monarch by his devotees.
It was a full display of the damnable syncretism plaguing Israel's worship. What could be more satanic than a religion that took to itself the name of the true God while at the same time professing devotion to his chief rival?
2 Israel’s highest authority, the one who they were calling on to hold them accountable to their promises to the Lord, was not Yahweh but Milcom. He was their king; the Lord was not. This was directly against God’s instructions, and Josiah’s reform sought to put an end to it (2 Kings 23:4).
5 those who bow down on the roofs to the host of the heavens, those who bow down and swear to the LORD and yet swear by Milcom,