Hos 4:15 Though you play the whore, O Israel, let not Judah become guilty. Enter not into Gilgal, nor go up to Beth-aven, and swear not, “As the Lord lives.”
Israel is warned against trying to draw the tribe of Judah into their folly. This warning serves the common good of keeping their sin more isolated, but it also is meant to protect the tribe which would eventually produce Messiah. The warning against swearing on the name of the Lord is meant to keep them from multiplying their own sin by promoting the mix YHWH worship with Baal worship. This mixing, called syncretism, is even worse than pure idolatry because it reduces YHWH to the level of and equates YHWH to false gods. Syncretism profoundly violates the first three of the Ten Commandments. It particularly violates the Third Commandment by reducing God’s name (taking the name YHWH in vain). Hosea was sternly warning not to draw Judah into this same sin.