As I’ve talked with various other DMs, the question comes up over and over: “Should you limit the available options for character creation?”
The answer is a resounding: “Maybe…!(?)
As with most other issues, this is one that’s largely subjective, so rather than give you a definitive answer, let’s look at a few related subjects first.
Experience
Ask just about any DM and they will probably tell you that there’s a big difference between playing with people who are new to the game and people who are veteran players. There’s pros and cons that might go (broadly speaking) with both, but the simple fact is that by and large, new players are struggling to grasp general game rules, racial features, and class abilities all at once, and frankly, they’re likely to make a bit of a hash of it all.
This means that they’re likely going to need help understanding it all, and having to flip between multiple books (let’s say Player’s Handbook, Volo’s Guide to Monsters, and Xanathar’s Guide to Everything), isn’t going to help things much. In fact, it’s quite likely to cause them stress, bog down your game, and irritate everyone else.
Which is all ultimately going to fall on you: the DM. You are the arbitrator of rules, the repository of knowledge, the one who’s in charge of the game, and your players are going to look to you to help them resolve their gameplay issues, which may end up with you digging through various books to find the answers yourself.
Alternatively, you may have players who understand the core rules and are able to adequately decipher the traits and features of new races without any help. The same goes for the DM. You may in fact know all of a characters abilities by the end of the first session and hold that information securely in your head without any trouble at all.
Campaign Setting
Not every race actually makes sense in every setting. Yes, you can play a warforged who somehow got planeshifted to Forgotten Realms or Ixilan, but that doesn’t mean that the DM wants you to.
I have a friend who’s working on a campaign that, simply by it’s storyline, will only allow PHB races. Goliaths, Firbolg, and minotaurs don’t necessarily fit in just anywhere.
In cases like this, the DM should (if them deem it proper) absolutely limit options because it maintains the cohesiveness of the story, the context of the campaign, and the flavour of the setting.
Campaign settings are (at least in my mind) about crafting an immersive and full-bodied gaming experience. This experience can be easily diminished if the setting is disrupted by elements that feel foreign (although in some cases that may be the point).
Balance
I’ve touched on this before when dealing with characters with a fly speed, and it can apply to other abilities as well. Genasi and their inherent abilities come to mind almost immediately; interesting backstory options, creative abilities to use, overall balanced fairly well, but in the right (or wrong, depending on your perspective) campaign module, they can potentially wreak havoc.
In my opinion, a DM should take stock of the campaign fairly thoroughly before providing players with their character options.
I want to make clear that racial options are not the only considerations here, either; in fact, class options, typically multi-classing “power builds” are probably the biggest issue, but I’ve spoken about that elsewhere and don’t want to harp, just to bring it up to broaden the point somewhat.
In the End:
It’s your call. You, as the DM, are the one in charge of the game, and the one who will most have to live with the repercussions of your decision, and it is your decision to make.
Don’t be afraid to ask for honest opinions from your players. Know ahead of time what kind of game you want it to be. If it’s a printed campaign and you know someone else who’s run it, ask them their opinion. Be clear with your players, and honest, but don’t feel the need to get into specifics. When someone asks to play as a water genasi, you don’t need to tell them that there are a lot of bodies of water in the game that serve as barriers and traps, or that underground streams could act as shortcuts past a number of encounters and traps and make things too easy, just tell them, “Sorry, no. Not in this particular campaign, but maybe in the next one.”
Be clear, be honest, be wise, and above all, have fun!