The Balaamites of Pergamum and Jezebel in Thyatira have the same teaching. Both entice the saints to fornication, which much be a spiritual form of adultery, and to each things sacrificed to idols.
These twin sins link back to the apostolic decree after the Council of Jerusalem, which forbade Gentile believers from eating things sacrificed to idols and from fornication. Here the connection is reinforced by Jesus’ statement that he lays “no other burden” on the Thyatirans (v. 24; cf. Acts 15:28).
Balaam and Jezebel are both encouraging violation of the apostolic decision. The Council of Jerusalem dealt with the issue of Judaizing. Circumcision and conformity to Jewish dietary restrictions and purity rules are not to be imposed on Gentiles. But Gentiles have to keep certain rules that are quasi-ceremonial, in deference to the Jews who make up the bulk of the church.
This is a fundamental danger to the gospel, not so much because the Balaamites and Jezebel’s children are “libertines” in some generic sense. The problem is that both have been violating the Gentile restrictions and thereby endangering the union of Jews and Gentiles in the church. Pressure comes from the Judaizers who want the church to keep Torah; pressure is also coming from the other end, from Gentiles who don’t want to conform to the decision of Jerusalem.
Together, these “heresies” endanger the achievement of the gospel, the one new man knit together by the cross of Jesus.