The Eberron setting book just came out, which has a few new character options, including dragonmarked subraces, and a variety of new gear.
But the setting doesn't change the core mechanics of D&D.
The original Dragonlance mostly forbid divine spellcasting, and tied wizard magic to moon phases. Dark Sun had defiling that caused magic to suck the life out of living things, creating vast swaths of desert.
Check out the optional rules in the DMG when it comes to planar travel. If you based a campaign entirely on another plane, that world's planar traits would alter some underlying assumptions of the game. An all-shadowfell game might have you dealing with 'shadowfell despair' every day. If the whole campaign is in Arcadia, then the 'psychic dissonance' optional rule would basically force everyone to be LG or LN, and the 'planar vitality' optional rule would make people immune to fear and poison.
Ysgard has an optional rule where anyone who dies there resurrects the next morning. That would upend a lot of assumptions about how to play the game.
Have you ever played in a setting where the rules of reality weren't quite the same as the default of D&D (or of whatever ruleset you were playing)?
In the ZEITGEIST adventure path, one of the minor traits of the world is that gold rings block teleportation. If a person is wearing a gold ring, they can't teleport. If you surround a jail cell with a gold ring, someone can't teleport out of it.
Two other traits of the world restrict the duration of magical flight to five minutes, and prevent summoned creatures from sticking around for more than five minutes. All of these have reasons behind them that matter to the plot of the adventure path, and they're fairly minor.
But how far can you step away from default rules before you get uncomfortable?
Would you accept an Ysgard-style game where it's impossible to bleed to death, but death is still possible if someone decapitates you (aka, Highlander)? What about one inspired by the video game Myst, where divination magic doesn't work on islands? If you've watched the TV show Supernatural, salt actually drives off ghosts, and other mundane tricks can protect you from monsters, which might be a fun way to give low-level adventurers tricks in a setting with lots of horror tropes. In a game inspired by His Dark Materials, would you be cool with each PC having a bonded familiar? What if the GM handed each player a copy of their 50 page setting bible, said, "You're all proficient in History as a bonus skill, so you have to read this"?
I've been playing D&D for 23 years. I like trying new things. But how far is too far?
Very good topic, check out how I fought with my homebrew darksun conversion trying to be true to 2e flair so far. It covers things like weapon out of worse material, halfgiants, defiling and it really gave me headaches to find solutions which do not clash with 5e core mechanic.
I cannot tell you at which point the core mechanic absolutely breaks but I can tell you which things do not break the core mechanic:
Restriction of race, class/subclass, alignment and any combination of these do not break anything at all since they are pure fluff.
Restriction of equipment does not break anything if you still have viable options e.g. you need some decent weapon and armor for your fighter or you have to take that into account when building mobs and encounters.
Restriction of spells above 5th level should not break anything, it might shift the class balance a bit though, I would not recommend it for lower levels than 6th and up. Especially spells which allow magical movement and shenanigans can be cancelled without problem.
Otoh Restriction of spells as such does not break anything, if you cover the basics. Means there should eventually be some cure wounds spell for your cleric, but it is not needed that he can cast heat metal.
Again even if some will not believe me spells are fluff also, not basic mechanics.
Now some of the difficult things:
Environmental stuff like weather conditions, planar specialities etc. older editions used to cover this with a busload of pus and minus modifiers. You cannot do that with 5e. It does indeed break the mechanics and the flow of the game.
So what to do here? There is no fix rule that I would recommend but the following is what I would do:
Is something really hefty let us say a sandstorm or a blizzard then you can apply disadvantage to some of the characters actions but do not forget every advantage from what source ever cancels that one out in 5e. and disad is like a -5 which might not be the level at which you wanted to rate some nuisance.
So work around these things, e.g. Party is under a constant bane (-1d4 on attack etc) for some shadowplane.
Or : nonmagic weapons do -1d4 damage here or not getting a short rest in some shelter every 4 hours gives exhaustion
With DL as far as I can remember they had no cleric spells in the beginning but the blue crystal staff which worked like a spell store of cleric spells with charges recharging daily. You can absolutely have a cleric who got no spells at the beginning have such an artifact instead until he gets some spells the normal way without breaking 5e. You only have to adjust the artifact so it is not to powerful.
Dragonmarks / wild psionics instead of feats? no problems
Moon magic? easy, this one shouts for advantage/disadvantage for saves, spell attacks etc. np at all here because it is a temprory condition.
Cannot think about more atm. hope that helps