Racial Continuity

Why do some races change drastically between settings, but others stay more or less the same?

Name one outside of humans.

The reason every race but humans see shifts in design is because a writer wants to use them for a specific task.

Good question.
A thing to note though is that Lotr Orcs are more similar to modern Goblins then modern Orcs, to which Tolkien's Uruks are more similar.

And as for Orcs seeming mutability, i'd say that it's really more cosmetic than anything else. They where and are more warlike and savage then humans and because of that live closer to the land and are often nomadic, tribal or raiders.

Dwarves.
Pretty much all dwarves in any setting are grudge-bearing beer-drinking, axe-wielding, mountain-dwelling bearded blacksmiths with scottish accents, with the variations between settings amount to little more than a different coat of paint.
There are a few exceptions, most notably TES dwarves who are actually elves (their proper name is dwemer, or deep elves, and the name "dwarf" is probably a mistranslation), and also extinct after they build a giant robot that literally noped them from existence, but they're few and far between.

Aside from the example you posted, I can't think of many examples at all where races change drastically between settings. Only other kinds I've seen are occasionally when an author gets it into their head they want a story that makes orcs not the bad guys but they make them look a bit less human to emphasize the difference.

Different eras of fantasy being put next to one another.

Tolkien "orc" was interchangeable with goblin, and there were different breeds with different levels of strength and resistance to sunlight. The Uruk-Hai were half-orcs

Early D&D orcs were pig men, and then were changed to neanderthal looking guys as time went on.

Warhammer combined the pig and neanderthal looks, and brought in the green skin and red eyes.

Warcraft gave the explanation of the green skin as corruption from demons, and later codified a wider trend of Orcs as a separate faction from the normal 5 Races that could still be considered good guys.

There, a shortened essay on Orc history.

Because Tolkien, the father of modern fantasy, expanded on more races more than others. So while we have a detailed, captivating, and rich history for dwarves and elves in LotR, we don't really have one for orcs or hobbits. So when someone is making a setting they can use Tolkien's archetype (Tolkien is a master of worldbuilding, it'd be hard to pull a rich cultural history out of thin air to rival his) for some races but have to invent their own. This is why we have different backstories, cultures, and related races for halfings/gnomes and orcs/goblins; there was none to pull from Tolkien's work and none have really met up to the gold standard that is Tolkien's world building.

I wonder, if Tolkien had lived longer, if he'd have made a long compendium about all the things that happened in the Shire. That would've been nice.

...

not on Kaladesh