In his typically forthright way, Gerald Ronson, the president of the new Jewish Community Secondary School, explained the reason behind its opening next year: “It is important that in our community we do have a first-class faith school which will take on board non-halachic, together with halachic, children,” he said in a YouTube interview, adding: “It’s not me that makes the issue of whether you are halachic, non-halachic… You want to go to a Jewish school? You should be able to go to a Jewish school.”

There are two things to say about this. The first is that a large swathe of Jewish public opinion shares these sentiments and cares little for distinctions between “halachic” and “non-halachic” Jewish children.

The second is that, from a traditional view, the word “non-halachic” is meaningless. Classical Judaism is built on distinctions, between Shabbat and weekday, kosher and treif, meat and milk. According to Jewish law, you are either Jewish, or you are not.

But, in today’s Jewish world, the term “non-halachic”, of course, is far from meaningless. The new coinage describes a contemporary social reality — the growing body of Jews who are accepted by many of their fellow-Jews but not by Orthodox rabbinic authorities.

The recent legal battle over the entry policies of Jewish schools in this country is simply one instance of a global fracture. For all the books and symposia, speeches and articles, there is no immediate solution to divisions over who is a Jew ,and the hope of finding a common standard now seems messianic.

Israel has created a different source of authority to Halachah

Differences over Jewish status stem from several factors. Conversions performed by Progressive and Masorti rabbis are not recognised by Orthodox rabbis. American Reform and British Liberal count the children of Jewish fathers and non-Jewish mothers as Jews (providing the child is raised Jewish). Then there are non-synagogal secular or cultural Jews who may also be of patrilineal Jewish descent.

Add to this the impact of Israel’s Law of Return which grants citizenship to any Jew from the diaspora who wants to “come home”. For the purposes of the law, a convert is Jewish regardless of whether the presiding Beth Din is Orthodox or Progressive. In effect, the state of Israel has created a different source of authority in the modern-day Jewish world to traditional halachah.

But there is more: the Law of Return also grants entry to the child and grandchild of a Jew. So that the unconverted child of a Jewish father or non-Jewish mother can still claim the right to settle and become part of broader Jewish society in Israel, a de facto Jew — which is precisely what has happened with hundreds of thousands of East European olim over the past 20 years.

On top of all the political and religious differences between Jews, the disagreements over the very definition of Jewishness make it hardly surprising that Chief Rabbi Sir Jonathan Sacks could write, in his latest book, Future Tense: “I see a Jewish people as divided as it was in the last days of the Second Temple.”

Just over a decade ago, it seemed we were on the verge of a breakthrough in agreeing a universal yardstick for conversion, at least in Israel. Great hopes were held out for the new conversion institute, which was created in 1998 with interdenominational backing, following an Israeli government commission: its courses would include Masorti and Reform as well as Orthodox tutors, although the actual conversion would be validated by special Orthodox courts. However, its success has been patchy and it has not been helped by doubts cast by parts of the Orthodox rabbinate over the integrity of its conversions.

Arguments over conversion boil down to this: the level of religious commitment demanded of converts. At conversion ceremonies in the Israeli Chief Rabbinate, the convert declares: “I undertake to be a loyal member of the Jewish people and uphold and fulfil all the mitzvot of the Torah and all the mitzvot of the sages…” For most Orthodox rabbis, this entails taking on a fully observant life.

Alter the formula, however, from “all the mitzvot” to the vaguer “mitzvot” and you might allow some wiggle-room for the non-Orthodox. A few Orthodox rabbis have challenged rabbinic consensus by arguing for a more pragmatic conversion policy in the interests of national cohesion, which would expect only a commitment broadly to Jewish tradition rather than a devout lifestyle. But the tendency in the Orthodox world at the present time has been towards stricter rather than more flexible conditions for conversion.

However irreparable the rifts appear, the notion of Jewish peoplehood is not quite done for yet. Religious denominations may continue to differ over Jewish status, over who can join a synagogue or marry. But beyond the synagogue walls lies a wider Jewish arena with more open doors.

Beneath the umbrella of cross-community organisations, such as Maccabi, Limmud or the UJIA, sectarian differences can be laid aside and Jews of all kinds, halachic or non-halachic, can equally take part. It is in these institutions of civil Jewish society, rather than narrower religious frameworks, that the idea of Jewish peoplehood can be played out.