This is something that I have seen cast about by various DMs over the years - sometimes even by myself. D&D is filled with a menagerie of races and creatures. Sometimes, too many. This can often lead to the DM’s knee-jerk reaction “Not in my campaign!” or “That doesn’t fit my world!”, generally with the modern thought of “if I allow one, there has to be others like it.” or that there needs to be whole backstory of a race/culture for how it came to be in the game.
So, not wanting to squeeze in, say, a Dragonborn city/culture into one’s campaign, the whole race is banned from the campaign. I do think that can be a mistake (on these grounds), and it comes from a bit too modern understanding of our world.
Monsters - and most especially player characters - don’t have to come from a species. From acts of the gods, magical experimentation, cross breeding or accident the creatures of D&D and its races can range from being unique to a mere handful, instead of a globe-spanning race.
That means a variety of things, primarily that you can allow an element into the game - a player race, a monster, magic item or whatnot once, and you don’t have to change your entire game world to allow it exist.
An owlbear, could, for example be a singular, unique magical crossbreed that exists only in that one dungeon you run rather than a race scattered across your game world. Just because the MM stats it up like a “it must be a Tuesday” encounter does not mean that such creatures run rampant everywhere. Perhaps Mort the Mage has the only version kept in status in his basement. Maybe, he made a couple and they got loose, running around in the woods near his dungeon. Perhaps they’re all male, and will die out from old age. If its able to mate, maybe the result is only a (giant) owl or a bear - not an owlbear, so the species can’t propagate.
You could follow mythology with some monsters; there might be only one Medusa in your world, or one chimera or even (gyno)sphinx - and it doesn’t necessarily have to be a super-high level threat; its uniqueness can play out in other ways besides sheer power. Sometimes, things stand out just because there IS only one of them in the world. It could even be that there’s only one in existance at a time, and only when the current one die does another come into existance, rise from the corpse of the old one or reincarnate some time down the road (and seek out its killer…). Mayhaps, even at some point during its life cycle (or death) it morphs into something else that no one has ever seen - or ever will see again.
You could let the one player who wants to play a lizardfolk in your party by having the PC’s background be that they were once an elf, but after crossing a hag in a swamp, she transformed the unfortunate individual into a “hideous” lizardfolk for their insult. Even if there are NPC/evil lizardfolk in the game, the PC has no connection to them, and might very well be treated as an outsider to a “native” of those races. As above, it might not be able to carry its traits on to any prodigy it happens to create, or such prodigy may be sterile leading to a species dead end (or perhaps an epic quest to allow their species to continue and grow…).
The warforged someone wants to play could have been a unique wizard’s construct who outlived their master, and gained sentience - in a sort of Frankenstein’s monster or I, Robot (the Will Smith version) or Full Metal Alchemist scenario for that matter. Likely, it can’t create others of its kind, and it will fade from the world when it passes on, never to be seen again.
As a last note, there’s nothing wrong with not putting a creature or race into a campaign because its doesn’t fit the theme the DM and players are looking for - Kender in Dark Sun, for example, would seem quite absurd. The idea though, is to relax the grip a bit on the purity of the “world” the campaign is set in. There’s nothing wrong with one-offs, and you don’t need to twist an established world to work in something out of the ordinary. Heck, sometimes you don’t even need to explain it - and just let it happen and let it either be a mystery or let someone else come up later for a reason why it happens/works.
