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>The accusation that the synagogue was a synagogue, not of Judeans but of Satan is connected with an internal dispute on how one faithful to Israelite traditions should live with the Roman economic system. The author of Revelation was arguing that there should be no compromise with Rome, and those who did compromise were not fit to be called Judean. The Synagogue, on the other hand, argued that peaceful coexistence with Rome was possible. It is suggested that the synagogue accused members of the church in Smyrna of not being Judean because they refused to pay the special Judean tax that allowed them to practice their religion unmolested. For the author of Revelation, however, to pay the tax would be an act of apostasy, as the tax paid for the rebuilding of the Capitoline temple.
https://journals.sagepub.com/doi/10.1177/014610799902800405