Synagogue of Satan?

This is based off of Revelation 2:9 where some peope interpret it as Jews being the Synagogue of Satan.
Elaine Pagels in her book Revelations suggests rather a different interpretation:
As John saw it, Paul’s converts were not like the Gentiles whom Jews had called “those who show reverence for God” and who had long sought to join with them to worship their God. Those old-fashioned Gentiles had known their place, keeping a respectful distance from those born Jews, since they realized that gaining full access to the Jewish community would require them to change their whole way of life. Men would have had to undergo surgery to become circumcised; both men and women would have had to adopt sexual, social, and dietary practices that would separate them from their former families and friends before they could qualify to join God’s holy people.

By contrast, some of Paul’s converts were saying that, having been “baptized into Jesus Christ,” they were as good as those born Jews—maybe even better. John, who sees Israel’s privilege linked to the obligation to remain “holy,” is angry that they claim to belong to Israel while ignoring what the Torah requires. To justify such negligence, these “would be Jews” invoke the authority of the famous—or, John may have felt, infamous—missionary Paul, self-professed “apostle to the Gentiles.”

Even worse, from John’s point of view, is that instead of respecting Israel’s priority, such newcomers speak of themselves—and Gentiles of every kind—as if they themselves were Jews, claiming both Israel’s name and her prerogatives. John seems to have such people in mind when he says that Jesus told him to tell his people in Philadelphia that “those who say they are Jews, and are not, but are lying,” are nothing but a “synagogue of Satan.” John adds that Jesus assures his true followers in Smyrna that he knows what slander such people sling at them: “I know the slander on the part of those who say they are Jews and are not, but are a synagogue of Satan.”
John W. Marshall, in “John’s Jewish (Christian?) Apocalypse” (in “Jewish Christianity Reconsidered” Fortress, 2007), spends some ink on “the synagogue of Satan”:
“John does not specify the precise conflict in a way that clarifies the historical situation. It is necessary, however, to understand what John does and does not say. He does treat the term ‘Jew’ as one that belongs to him. He does not portray the dividing line between the group he favors and the group he opposes as the line between Jews and Christians. Most importantly–and contrary to the best efforts of biblical commentators–he does not make beliefs concerning the divinity or the messianic status of Jesus the issue that divides him from his opponents; no argument over christology is in view. What we learn from John’s slander of these two groups is that he is completely invested in the traditional Jewish abstention from idol worship and that he considers ‘Jew’ as a designation that belongs to him and his community. The line he draws in 2:9 is not a line between Christians and Jews, and according to John, the people he slanders are not Jews.
“John, in other words, is committed to Judaism through and through. He makes no clear criticism of Judaism or of other Jews as such. His rhetorical work is directed to helping his Jewish community live in relation to the Greco-Roman world, but unsullied by it. He gives no indication of self-consciously intending to represent a sect of Judaism rather than the whole. Unlike Paul, who positions himself as a Jew living outside Judaism for the sake of Gentiles (Gaston, 1987, Gager, 2000), John’s primary axis of solidarity is with Judaism. His program addresses the means by which Jews of the Diaspora ought to remain faithful during the trying circumstance of the Judean war–by separating themselves from the nations and the work of the nations, which implies subordination to the satanic power of Rome. At the same time, John stands within Judaism in imagining a massive influx of Gentiles. Unlike the Gospels of Matthew, Mark snd John, the Apocalypse has no anxiety over its position within Judaism or obvious animus against other groups of Jews. It is not striving to claim its place against other sects or social institutions. Unlike the Gospel of Luke and Acts, John’s Apocalypse does not stand outside Judaism naming Christianity as a distinct entity and picturing it laying claim to the legitimacy and antiquity of Judaism while at the same time superseding it. While John’s Judaism is certainly atypical in its focus on Jesus as the Lamb of God who will initiate the eschaton, vindicate God’s people, and draw in an innumerable number of Gentiles, his rhetorical position does not limit him to solidarity only with those who share the peculiarities of his theology.”
David Frankfurter writes the following on page 469 of The Jewish Annotated New Testament:
Who are “those who say that they are Jews and are not,” who are rather a “synagogue of Satan” (2.9; 3.9)? Interpreters have customarily assumed that John, a “Christian,” would have viewed true Judaism as Christ-devoted, and thus that these so-called Jews must be Jews who ignored or denied Christ. John would then, in effect, be pitting himself against the (non-Christ-devoted) Jewish community as radically as against the Roman Empire (chs 17–18). Some Christian exegetes have proposed, in fact, collusion between Roman authorities and Jews in persecuting Jesus-believers, for which there is no reliable evidence. It is important to recognize that nowhere in this text does John juxtapose himself to Judaism or Jewish traditions. Indeed, his specific opponents in this part of the book appear to espouse not Jewish teachings but rather the diluted interpretations of meal and sexual purity laws we associate with Paul of Tarsus (2.14,20; cf. 1 Cor 7–8), and even the mega-enemy, Rome, is described in terms of female sexual pollution (17.4–6). Elsewhere John adheres to the strictest concepts of Jewish purity, those associated with the Temple priesthood and comparable to the laws of the Qumran Essene community (12.17; 14.4; 21.27; 22.14). As we consider John’s profound commitment to Jewish purity in combination with the increasing popularity of Pauline teachings among Gentile God-fearers in Asia Minor over the later first century, it begins to make more sense to take John’s polemic against so-called Jews in plain terms. Thus, he declares that those Gentile God-fearers claiming an affiliation with Judaism as a basis for Christ’s salvation (cf. Rom 2.17–24,28–29) are in fact not Jews at all. “Synagogue of Satan” in this case refers generally to an assembly (Heb edah) rather than a building or institution, and as often used to denote a collective opponent, as at Qumran (1QS 5.1–2, 10–20; CD 1.12; 1QM 1.1).
Thus, notwithstanding the phrase’s anti-Semitic history as a condemnation of Judaism, John means “synagogue of Satan” only as a rejection of those pretending to be Jews. The real Jews are the ones who, like John and his confederates, cleave to a strict, priestly interpretation of purity laws.