Orthodox churches are kinda special in the sense that they're very oecumenical, don't go around saying "XYZ isn't true Christendom", venture outside of their territory only carefully (e.g. to serve migrants who happen to be orthodox, but actively avoiding becoming a promiment church in those areas), but OTOH also tend to be staunchly conservative when it comes to their own traditions. They're not centrally-run like the Catholic Church, while Constantinople holds a special place individual territorial churches are self-ruling.

So when e.g. Lutheran Churches say "Everyone is a priest, so obviously women too can be reverends", Rome is writing bulletins warning their own believers of participating in "so-called sacraments" in "erring churches", whereas the Orthodox go "nah we're fine as we are, thanks but no thanks".

Splitting off from Moscow is indeed political, also, complicated, also, partly theological (because ecclesiastical jurisdiction), there's two major branches: The re-constituted old Kiev patriachate, dating back to the 90s, (Moscow back in the days dissolved it without even asking Constantinople which readily accepted the reconstitution), and an organisational arm of the Moscow patriarchate which declared independence form Moscow in the wake of the invasion. That's also the one with the spy monks though not all of that "we're independent" talk is necessarily a front the church has, aside from political hacks, also actually religious people in it. Shocking, I know.

Switching to a different calendar is theological but Constantinople certainly won't care short of saying "nah we're fine". It's, after all, what "autocephalous" means.