On the topic of lack of asymmetry, I think religion is pretty unsatisfactory in Civ. Realism Invictus doesn't try to rock the boat too much in regards to that; it expands the content of the ingame religion and gives you a few more ways to interact with it, but doesn't alter how it really functions. The History Rewritten mod actually does a much better job in that respect, allowing you some discretion over how your chosen religion functions and being the product of great prophets, effectively backporting large portions of the Civ 5 religion system into 4 with some limitations and alterations (religions are actually defined in History Rewritten, with each religion have different basic beliefs - e.g. Christianity is Monotheistic, which has distinct bonuses from Confucianism's Ethicism), but in detaching it from the tech tree (and throwing in a bunch of pantheons) it detaches religion to the point where they're interchangeable. Religions, like civilizations, are not interchangeable and will fracture over time; they also greatly inform civilizations to the point there's chicken and egg arguments over which creates which. Imo, an ideal religion system in civ would be a mix of Civ 5/6 with Old World (which built on 4's ideas of religions not being fungible); every civ should have the option to get some sort of pantheon which is entirely theirs, while religions aren't just founded out of the ether and have core, unchangable tenets, and are also limited in number. Religions should eventually schism as their tenets develop, allowing players that didn't found a religion to still found their own denomination (up to a certain amount) to make them more customizable as the religion spreads, and also offering distinctions between coreligionists and heathens for the purposes of religious management. I do find it funny how religion was left in the dust as Civlikes started trying to make civs more interchangable; it wasn't even a mechanic in Humankind until a few patches after launch.
I tried out History Rewritten because of this post. My thoughts on the matter largely match yours. I really did not like how there was seemingly a religion for every civ in an 18-player earth map, especially as most of them started out identical and only shifted over time with techs. Major religions should be rare (I'd use number of civs/3) and not only non-fungible, but having the potential to massively change your game. Civ 5 multiplayer does a decent job of this, as each tenant and pantheon can only be chosen by a single player, it creates a real rush for being the first or second player to a powerful religion before the good tenants run out. Against the CPU, this doesn't work as well.
I'd also agree with Pantheons having an impact, and I think Civ 5's pre-religion is their best addition to the system, but every major religion had different reactions to what came before and how, if there was any, syncretism impacted the faith. I'd argue that IRL religion plays the single largest role in societal development, and that converting to a religion should have as much, if not more, effect on your playstyle than even picking your civ. Here's some spitballing for what a proper Civ religious system should look like:
Pantheon: You take this from Civ 5/6, representing your pre-axial religion of choice. Then you found certain religions either through techs or through faith accumulation, all with vastly different bonuses depending on your early game.
The Religions themselves:
Hinduism: The only religion that allows you to keep all your pantheon traits, as Hinduism is basically Indian paganism given a fancy name. Since it's just a refinement of your Pantheon, it serves to double/vastly increase the effects of it. Hinduism can be extremely useful as a first religion if Pantheon traits are first-come-first-serve, and you selected ideal traits that scale extremely well. The other way would be for you to add even more Pantheon traits well beyond everyone else.
Christianity: The perk here is that you unlock the Apostolic Palace from Civ 4 (barring the diplomatic victory option), the palace can vote on crusades, blockades, truces, and give bonuses to the controller and it's members. This serves a diplomatic game extremely well and gives incentive to spread your faith around to use it as a sword and shield, with the adverse effect of losing control if you piss off all your brothers in the faith. But spreading the faith further serves to add to the bonuses given by the AP.
Islam: The Caliphate is given to the most powerful Muslim nation, any muslim nation of low enough score relative to the Caliph automatically becomes the Caliph's vassal, with the issue that any fellow Muslim civ that isn't weak enough to become vassalized will try to take you down. You want to spread this faith by sword-point, preferably yours, instead of converting other large empires. The best religion for closing out a conquest victory thanks to the vassals.
Judism: Immense bonuses that increase as you spread your faith to other cities, but weaken as other Civs adopt the faith. You play a strange balancing act between having a large diaspora to benefit you, but not letting in others into the club to dilute your internal cohesion, all the while keeping the gentiles happy enough that you don't get run over for being an infidel.
Buddhism : This one depends the most on what kind of Civ game we're running, but I was thinking of monastaries providing unique yields to tile workers, or to specialists. I'd really lean in on the variety to produce warrior priests (Sohei), mass missionary movements ( Buddhism's pread from India to Tibet to Mongolia), and other benefits that monks provide. Buddhism should be the min-max "chose your own bonus" religion that is the most flexible of the bunch.
Zoroastrianism: I have no clue here but it's my pick for the final of the 6 big deal religions, as Confusanism and Taoism aren't really religions, and Shinto, Voodoo, Astaru etc are just fancy names for the local pagan practices.
All of these can carry over some of the former Pantheon to differing degrees, from not much (The Abrahamics) to some (Buddhism and Zoroastrianism), with Hinduism carrying over everything and expanding.
Useless theory crafting, but just to give an idea for how you can make religion incredibly impactful and worth grabbing, instead of largely interchangeable or customizable.
