I like healers, I like spell casters, and I want the cleric class to work well.
I even like human spiritualities, I like mysticism, I like monotheism, I like animism, I like Buddhism, I like Daoism − when the cleric class looks more like the religions of many different kinds of ethnic groups, I like it. The 3e cleric supports ethnic diversity for religious traditions. I like the 3e cleric.
But, I repeat, are you playing AL? Because otherwise what AL does or does not is irrelevant to the conversation.
And while you may like playing with spirituality and mysticism and animism… you still need to fit the campaign setting. If the DM is okay with you playing a cleric to a totemic spirit then that's fine. If the DM isn't okay because clerics of causes don't fit their world, you shouldn't be able to wave the PHB in their face and say "But the RULES say I can be a cleric to a cause!"
(Anecdote here. While I believe you want to be a cleric of a cause because of your knowledge of other religions and types of spirituality, this wasn't universally the case. In 3e, I saw quite a few people opt to be clerics of causes so they could be clerics with not having to obey any dogma or restrictions and just murderhobo things up. )
The 5e core rules arent working for me. The 5e core rules saturate with unwanted setting assumptions. It is nonviable to spend weeks scrubbing out undesirable flavor from the text. I need *rules* that are setting rules.
Then don't use the 5e core rules.
Seriously. If 5e isn't hitting the right spots, switch to 13th Age, or Fate, or Genesys, or Cortex, or Fantasy AGE, or Cypher, or Pathfinder.
You have choices.
But… attacking on a game you don't like on a forum entirely dedicated to that game is not a good choice. That's like going to a barbeque and complaining about how you hate meat. It's not going to get a good reaction. And it's just going to derail any discussion being had.
For my purposes, I need it to be easy to create my own setting guide. I need to cut-and-paste the classes that the setting will feature, and the races that the setting will feature, the spell list that the setting will feature, the combat rules that the setting will feature. For example, cut-and-paste the cleric class, add a few sentences or paragraphs about notable religious traditions that the setting features, and then move on to the next thing that I need to think about when building an entire world. When the 5e core rules get out of the way of world building, this can be done in a single day − an enjoyable day. Creating a world is fun.
Combing to find and remove unwanted sentences or parts of sentences across many pages of core rules, is unfun.
Well, you can't cut-and-paste the PHB, so that's always going to be an issue.
The thing is, we're talking about flavour. Which is the easiest thing in the game to change. It's when the rules and tone of the mechanics are problematic that are far more of an issue.
If you want gritty realism or fragile characters or low magic then D&D gets in the way of the world. Because any changes need to be written and balanced and playtested and taught to the players.
Flavour is simple.
In my campaign setting, sorcerers gain their magic by drinking the blood or powerful beings with arcane power (celestials, dragons, fiends, etc), and barbarians are possessed with a primal spirit of rage that threatens to consume their minds and turn them into feral beasts of unceasing fury.
I'm not going to get mad at the rules of the game for not accommodating my vision of the class. The job of the book is to present the baseline and give enough flavour for rushed DMs to improv a setting on the fly.
Consider the player who wants to be a cleric in a setting where there are only nontheistic elemental mystical traditions. I unwant for that player to consult the Players Handbook that then insists on almost every page that the ‘gods’ are the ones who are the source of cleric spells. That dissonance is undesirable, that disruption to immersion is unacceptable. It ruins my fun of creating a world.
There are campaign settings without elves or dwarves despite the many pages in the PHB that insist they are a thing.
Again, no orcs or drow in Dragonlance, no gnomes and orcs in Dark Sun.
2e tied clerics with deities even more tightly than 5e and Dark Sun still managed to have elemental cults.
It takes ONE SENTENCE:
"The gods are remote and do not directly grant spells, although some clerics believe otherwise and insist they are the chosen champions of their deity, but agnostic clerics who do not follow the tenets of a divine power continue to demonstrate spellcasting."
Bam. Done. Suddenly, all the flavour in the PHB becomes unreliable narration from the believers.
3e has a legal core SRD that is setting neutral. I need that for when I play 5e too.
Your problem here is that you're comparing the 3e SRD with the 5e PHB. The 3e PHB is also full of gods and references to the Greyhawk pantheon, which is the default.
Instead, try looking at the 5e SRD. The term "deity" only appears 9 times in the cleric entry and the term "god" 5 times. Most of the latter in reference to sample gods, which can just be deleted.
Changing that should take a two minutes. Tops.
Now compare this with the 18 references to "deity" in the cleric entry in the cleric entry of the 3e SRD! Literally twice as many. And hard rules like "A cleric’s alignment must be within one step of his deity’s". That sure sounds like you *need* to worship a god. Deities are just as assumed by the class.
And pretty much every single spell that references deities in 5e does so in 3e.
Again, the differences between 3e and 5e are largely additive. The 3e book ADDS text saying you can worship a cause or philosophy. So your problem is NOT what is in the 5e PHB, but what is missing.
So copy that text. Just pull it from the 3e SRD and throw it into your documents. Because that's the difference.