In your text, it clearly refers to Jewish Orthodoxy because of terms like “kosher, kippah.” The term however in Judaism has a pretty vast connotation; by which I mean Jewish Orthodoxy is not a homogenous body of people; it includes different subgroups (Yeshivish, Masortim, Hasidim etc.) and sometimes gentiles actually use it to refer to Haredim too (which is not correct.) Orthodoxy in Judaism is usually about referring to historical precedence in determining what to do in different circumstances of life and the Halakha (the Jewish religious law) is considered to be inalterable and inalienable. Many of the currents that we actually recognize as Orthodox Judaism go back to the mid 18th century when several members of Jewish rabbinic body across the diaspora felt a certain discontent with what they believed to be the Western reading of Judaism that was rooted in Greek and Roman philosophy. As an alternative they decided to refer to the existing historical precedences. However, Orthodoxy is not only in Judaism. You have it in different religions and during the same period, many Christian and Muslim clerics started to have the same tendency. Look up Jonathan Edwards and the First Great Awakening in the British America before the US was formed. Also the emergence of Wahabism in Islam goes back to the same period. Of course, there is a sect in Christianity which is know as Orthodox and goes back to the First Schism in 1504 creating the Eastern and Western currents of Christianity. In addition, Orthodoxy is also in different political thoughts or in different human attitudes. So you could say like “Hippies had unorthodox views in the 60s.” Or “The Second Communist International was dominated by Orthodox Marxists.” Or like “Some people still have orthodox views about families” which in this case means they don’t recognize families with homosexual parents or single-parent families. I hope this helps and get back to me if you need more help :-)

I guess the author ment ex-orthodox= post orthodox. someone who used to be orthodox. In Hebrew, there is the expression datlash דתל"ש means a shortcut for dati lesheavar דתי לשעבר somone used to be religious. The education system for religious people in Israel is different from the non-religious one. So, even if you are not a religious anymore, growing up in a religious way still affect your character in some ways. :)

"Orthodox" here refers to a specific, strict branch of Judaism. There is a clue in the writer's (or character's) use of "kosher" just before. This is a word borrowed from Hebrew, with a clear jewish reference: kosher food has been prepared in accordance with specific jewish laws and traditions. https://www.myjewishlearning.com/article/orthodox-judaism/ https://dictionary.cambridge.org/dictionary/english/kosher