For me, a feat really only needs to come into play when you want to do something that is more powerful than what you could otherwise do.
That's kind of the definition of "feat."
1. An act or accomplishment of great courage, skill, or imagination; an achievement.
2. Obsolete A specialized skill; a knack.
If the word-salad lets you do something beyond the ordinary, something special, it's a "feat." That's more than a re-fluff. It should cost the player more than merely renaming something. By the book, if you want to take a feat, your DM has to allow it and you sacrifice the ability-score increase. So if the proposed "fluff" becomes a "feat" a sacrifice is in order.
Fluffing ends when the numbers change. Everything up to that point is just deciding if you want green elves or blue elves.
This is my rule of thumb also.
"Fluff" is a 5e Samurai. There is no mechanical difference between a RAW Fighter and a Samurai. You just call their weapons and armour by different names. It's still a Fighter using longsword and bow, and wearing plate armour. It's just that you call them "katana," "yumi," and "Ō-yoroi." The numbers don't change. About the only mechanics-specific feature I'd consider disallowing is if the player wanted to take the Eldritch Knight archetype.
Things can get complicated when the numbers don't really change, but the mechanics - how the numbers work, what they accomplish - change.
Like the above-mentioned cleric's armor of faith and hand-mace, sure, you can have that, but you you have to give up something, too. Like no longer have any armor or weapon proficiencies at all. You want to hit the fire elemental, you can't just switch weapons; you have to touch it with your bare hand. I think I'd also want them to give up more, like some spell availability, maybe restrict the domains they can access to one or two, but that's a discussion for another time/place.
There's already a workable substitute for armor - Shield of Faith. Works with DEX, too. But it burns a spell slot. I'd be okay with that. That's a sacrifice - to get the AC you want, you have to A. burn a spell slot, and B. possibly burn your first action in combat to cast it. Those are the cons. On the "pro" side, you get a free "cantrip" which causes 1d8+WIS bludgeoning and radiant damage which you inflict by touch. It's at least an attempt at balancing within the class itself, not really re-skinning or even fluffing anything.