Different issues arise with PC options and DM options. A PC option is there for the character's life in the campaign week after week. A monster can be there for one encounter. A PC option from a story perspective is much more important and impactful and for a race option should be more fleshed out than a monster option. If you have a PC rabbit folk it is generally more important to figure out how rabbit folk fit into the world so the player can play off of that more with their character. For a DM it is less impactful to have a one off rabbit folk encounter with the explanation made up on the spot to fit the situation or the explanation to be left a mystery.
That doesn't excuse the lack of world-building though if the goal is an internally consistent world.
A group of PCs encounter a gang of haregon bandits along the road. Ok, why are the bandits haregon? Are they natives of the area? If so, why have the PCs not encountered them before? If they are not natives, why are they here and where did they come from? Are the just refugees from a distant land, exiles from the feywild, or just a couple unlucky sods who stumbled through a portal from Gods-know-where? Why are they hostile? Are they feared, hated, or misunderstood? Could they have gone to the next town and gotten honest work if they wanted, or would they be perpetually shunned to a life of banditry on the outside of town? Are they inherently evil (or have a reputation to be)? What do the PCs know about them: lore, rumors, legends, or are they completely clueless? What happens when the PCs stop and parley with them or capture and interrogate them?
All that stems from one encounter. I guess if they act as one-dimensional HP sacks that fight to the death and exist to be defeated and looted, it doesn't matter. Haregon bandits replace goblins, orcs, elves, or human bandits and it works the same. But if the goal is internal consistency, it SHOULD matter.
Now, I think the same situation could easily apply to any PC as well. If a player came to me and asked "Can I play a haregon" I would have to ask the exact same questions. Are the natives or foreigners? Where do they come from? How do others think and react to them? There is trivial difference except perhaps the PC might need a greater amount of depth. (Or they may not, if the answer is "you fell through a portal" then the answer of where you came from is immaterial. What matters is you're here now.)
Which leads to a situation where most DMs punt on the question on where the NPC haregon bandits come under the hopes it won't matter, but don't on the PC haregon because it always will matter. My argument is "if you are curtailing things because they don't fit if your vision for the world, that vision should contain monsters as well." Otherwise, such curation isn't being made for consistency or vision as much as for personal taste masquerading as such. Which is a nice way of saying "if you're going to ban haregon, do it because you hate furries and not because you feel they don't match the tone of Greyhawk".
I have made (and will continue to make) exceptions for a world where there obviously IS a vision that is stated out the gate and is handshook on by all parties involved. If I say I'm running Theros, I'm under as much obligation to not put in a beholder as the PCs are in not playing a gnome. The goal is to keep to MTG and Greek myth species, and that should be respected. In such cases, the DM is under as much limitation in his options as the player is. This thread is really a good test to see when DMs opt to do this vs ones who use world building as a tool to limit player options without likewise limiting their own.