Can a Jewish couple married abroad get divorced in Israeli Family Court without going to the Rabbinical Court?

No. Under Section 1 of the Rabbinical Courts Jurisdiction (Marriage and Divorce) Law 5713-1953, the Rabbinical Court holds exclusive jurisdiction over divorce where both parties are Jewish. Even if you were married in a civil ceremony abroad, if both parties are recognized as Jewish under Israeli law the religious divorce — the Get — must be obtained through the Rabbinical Court before the marriage is fully dissolved in Israel. Civil property and custody matters can proceed in the Family Court in parallel, but the Get cannot be skipped.