Synagogue is originally the Greek word for a gathering or assembly.
It came to be used exlusively, almost, for Jews and Judaism.
This gives rise to a full understanding of the Revelation warning to beware of those who say they are Jews and are not, rather they are a synagogue of Satan. This refers to any ad all who claim to believe God.
synagogue (n.)
late 12c., "the regular public worship of the Jews," also the building in which this is done, from Old French sinagoge "synagogue, mosque, pagan temple" (11c., Modern French synagogue), from Late Latin synagoga "congregation of Jews," from Greek synagoge "place of assembly, synagogue; meeting, assembly," literally "a bringing together," from synagein "to gather, bring together, assemble," from syn- "together" (see
syn-) + agein "put in motion, move," from PIE root
*ag- "to drive, draw out or forth, move."
Used by Greek translators of the Old Testament as a loan-translation of late Hebrew keneseth "assembly" (as in beth keneseth "synagogue," literally "house of assembly;" compare
Knesset). Related: Synagogical; synagogal.