Another idea that thies to this second opinion is the quasi-marxist idea that similar material or political conditions will ALWAYS produce similar ideologies
I think you're right, with one caveat: similar material and political conditions
usually produce similar ideologies. That's the whole point of making realistic PODs: they change the material and political circumstances so that different outcomes can arise.
That, and it's difficult to think of an alt-Christianity...
That's lazy thinking. Most religious, philosophical, and political ideologies look nothing like Christianity. There is so much potential ground to cover!
I want to see more diverse TLs. I want to read about a Roman Empire that doubles down on the god-king concept from Egyptian theology that the early Caesars utilized, creating an Imperial Cult that claims the Emperor / Empress is a living deity and the physical embodiment of Philosophy. I want to read about how averting the destruction of the Second Temple causes the Empire to embrace Mahayana Buddhism. I want to read about Julius Caesar choosing not to demonize the Celts, which enables the spread of the Druidic priestly class across Roman Europe. I want to read plausibly weird TLs that start with small changes that impact the West in huge ways!
I also think it is because of the aggressiveness that Abrahamic religions have. Both Christian and Islam have at their core that to save people you have to convert them so wars and persecutions against other religions are something moral. You are literally saving these people from hell, there is nothing more moral than keeping people from burning in hell. Only 2 religions that I know of had such fanaticism and conversion strength, Christianity and Islam. The fact that they are monotheists also helps, being easier to organize things in the holy book than having +20 more gods. Catholicism for example achieves greater local interaction with saints. (both also have a martial culture involving them)
That's I think the most true. Christian and Muslim writers (as well as post-Christian and -Muslim writers) tend to have this concept bleed into their writing, so they imagine that different ideologies also would (or should) have a similar attitude towards ideological pluralism.