The Jewish representation isn't present until the third book, but I went and checked the dates and that's still before HDM (1990 vs 1995). Since I am Jewish, I never noticed the Church wasn't talking about Jesus enough and until Miriam appeared in the Secret Garden I just assumed that a different history of Protestantism meant no Oliver Cromwell which meant Jews were still banned from England.
The series is absolutely focused on how Christianity oppresses the in-group, rather than the out group. And part of that also manifests in Lyra's reflectively privileged position limiting our own view of the world.
But all this falls apart when you get to the Secret Garden. It's about Lyra's perspective being less limited and exploring more of her world. How far east does the power of the Church extend? Now where are the Jews!?
So my only remaining guess is that Scholastic thought mentioning Jesus by name or epithet was a step too far. Kind of like how Animorphs could do whatever they wanted but not included swears in text. Can't have anything that would make a parent freak out reading a page in isolation of the kid's shoulder. A less extreme version of the movie only using the term Magisterium instead of Church. Since the parents who ask for books to be banned generally haven't actually read the book, you can sneak all the subtle themes you want past them. It's the stuff visible at the surface level that causes problems. And Scholastic calculated that putting the name of Jesus and more direct quotes from sermons in the mouths of the villains would tip the scale from just having "extreme Christians" forbidding their children from reading the book to much more of middle america. Given how America is mostly protestant, you can get much further than you'd expect with an evil world spanning hierarchical church with an Inquisition and such; from what I've gleaned second hand from Eleanor Jenga talking about history education in the UK, the same applies in Britain. I know this is a pretty USAmerican focused perspective for a British book, but Scholastic is an American company and when you're publishing a book in English, they make up a larger audience.