On the second article Sara Hill comments: "The Rabbinate only has jurisdiction over Jews. I suppose the Imams have jurisdiction over Moslems and the Christian authorities have jurisdiction over Christians but I don't know the exact details."
What are the legalities of this? In particular, are Jews (usually by birth) and Catholics (baptised as children) subject to religious courts even if they are not religious?
The article "Enforcement of Religious Courts' Judgments Under Israeli Law" (Asher Maoz, Journal of Church and State 1991) is useful in understanding the legal underpinnings of this question. The beginning point is the Palestine Order in Council 1922 (this is from the UK Privy Council), where religion-based courts are established, so sect. 52 is about Muslim courts, 53 (later repealed) is about Jewish courts and 54 is about Christian courts. Section 53 was replaced with Rabbinical Courts Jurisdiction (Marriage and Divorce) Law, 1953, stating that marriage between Jews follows Jewish law, and says that rabbinical court has exclusive jurisdiction. Article 6 of that law allows a district court enforce a final judgment by a rabbinical court by imprisonment. Muslim courts similarly have exclusive jurisdiction over Muslims, though it is wider (it pertains to all matters, not just marriage).
Actual enforcement apparently involves the Chief Execution Officer. Basic Law 15 gives the Supreme Court supervisory power over all courts, including religious courts. So rabbinical courts don't have unfettered power to do whatever they want (under Jewish law), but there is direct state sanction of imprisonment as a penalty for not obeying a rabbinical court decision, there is non-religious execution of court orders, and there is secular supervision. Since civil marriage is non-existent in Israel, there is no choice (if you want to have the wedding in Israel) but to go to the recognized religious authorities, which seems to make Cyprus a popular wedding venue. A Roman Catholic divorce is not possible in Israel, a Muslim one is, and I really cannot tell about the various Orthodox Christian churches.
I cannot answer for other religions, but for Jews the answer is yes. That is a Jew is like a citizen of a country (such as the United States) and is therefore subject to the laws of that state. As a result, a Jewish man and woman are not legally divorced according to Jewish law unless the man has given the woman a get (jewish legal divorce). While the law you reference can only be enforced in Israel, it applies to all Jews no matter where they live. It cannot be discarded by the individual not matter how irreligious they might be.
Note that the legal term mamzer refers only to a child born to a married (by Jewish law) woman fathered by a man who is not her husband or to the product of incest (as defined by Jewish law). As such it is similar but not the same as the term bastard. Thus, if a woman who is married (by Jewish law) separates from her husband, but does not divorce him (by Jewish law) she is still married no matter what anyone else claims (including secular law). Thus, any children by another man are mamzerim and any second marriage is invalid. According to Jewish law, the first husband cannot stay married to her and must divorce her, while she is forbidden to marry the second man once she has been divorced.
