QuentinGeorge
Legend
It's rather easy to fit in dragonborn and tieflings (the two most mentioned races from the PHB), since Ravenloft has stuff from everything (Lord Soth from Dragonlance is in it). Of course, the CoS adventure was basically just Barovia and didn't include all the other demiplanes within the Mists. There's also the part about the adventure starting in Faerun, too. But I can understand the desire to not want something that was introduced in a later PHB to be included in an old setting. Like you said, it's easy to disallow the bird people, since they don't appear in the PHB. Just by saying "PHB only". But I have seen nerd rage about people wanting to play a tiefling in Grayhawk, or a dragonborn.
There's the big chance WotC would include some new NPCs of those races in a Grayhawk book, because they exist in the PHB. Just like how they kinda hamfisted the dragonborn into FR. If WotC would be smart, they'd leave those races out (are the dragonborn even included in the new Eberron book?), and have a little appendix on how to include those races into the setting if the DM is so inclined (kinda like how they did the same with the adventure books on how to place the adventure in a different setting).
Ravenloft has always been fairly "iffy" on how suitable are the races beyond humans, elves, halfelves, gnomes and halflings, most likely due to its 2nd edition origins. Notably the 3rd edition setting re-fluffed halforcs as "calibans", mutant humans caused by misuse of magic. You might even extend that to dragonborn - have them even more extreme forms of "calibans".
Now I know someone is going to try and correct me and say Ravenloft dates to 1st edition - and the original module does. But that is not the campaign setting. And that's the crucial thing. Curse of Strahd is a reboot of the original module, it is NOT the 2nd/3rd edition setting. It departs radically in continuity and tone in several important places. It doesn't even have the proper mechanics that the setting is known for. (Fear/Horror/Madness checks, Power Checks, Altered Magic, No contact with gods). Barovia in Curse of Strahd is not the Barovia from the Ravenloft setting without some radical retooling.
Those thinking that a 5th edition version of Dark Sun will ban any races are barking up the wrong tree. If they didn't take that approach with Ravenloft, or Greyhawk....why would they do it with Dark Sun?