Unearthed Arcana articles
The content of the Unearthed Arcana are designed partially for play-testing ideas and seeing where the fans are focused in class, race, and option design. They are all optional content that is designed for WOTC to perform surveys on, improve, and refine before a possible release either as a later form of Unearthed Arcana, or in books to be later sold. An Eberron source book has been hinted at by the direction of the First Unearthed Arcana entry and other information, but they are very vague hints and nothing concrete about their plans are known yet.
Adventurer's League characters
The documentation for the Adventurer's League is very specific about what content can be included in the character creation process, and for many reasons. Even within larger bodies of contents, such as the Elemental Evil Player's Guide, individual options may not be available to players. The Aaracockra is an example of this. Every season will have its own options available to players. These options will always include the Player's Handbook, and will generally include a Player's Guide for the season if one has been printed. Even class options from the Dungeon Master's Guide are generally not allowed (with very limited exceptions based on certs offered at conventions).
What this means
The bad thing about this is that no characters outside those that are discussed in the Adventure League Player's Guide is available for play in the Adventure League, and even within the sources that it allows you to use, you are restricted on combining options. It's not so much about unofficial versus official, as what they are allowing in an organized setting specifically.
As an example of restrictions placed, the Sword Coast Adventurer's Guide is allowable for all story lines, but can not be used in conjunction with the Elemental Evil Player's Guide, even if the character is from the Elemental Evil story arc.
Currently there are no Unearthed Arcana entries even mentioned in the AL Player's Guide, so you cannot use the options presented within any of them. It is highly unlikely that any Unearthed Arcana entries will ever be present in AL, since they are considered to be in draft form. When the options are refined (assuming they are not scrapped), they will become available through official releases such as the Elemental Evil Player's Guide and the Sword Coast Adventurer's Guide.
There are two different ways a race could be "official": it could be "official" in the sense of fully-tested and legal for sanctioned organized play campaigns, and it could be "official" in the sense of being published in 1st-party material from Wizards of the Coast. Which one is relevant depends on why you're looking for an "official" race.
Sources:
BR: Basic Rules, Chapter 2: Races
SRD: System Reference Document, 5e, "Races" at p. 3-7
PHB: Player's Handbook, Chapter 2: Races
DMG: Dungeon Master's Guide, "Creating New Character Options" at p. 285-287
AI: Acquisitions Incorporated, "New Race: Verdan" at p. 72-74
EE: Elemental Evil Player's Companion, Chapter 1: Races
GGR: Guildmaster's Guide to Ravnica, p. 12-21
MToF: Mordenkainen's Tome of Foes, throughout Chapters 1-5
MOoT: Mythic Odesseys of Theros, Chapter 1 > Races
LR: Locathah Rising, an Extra Life fundraiser from WotC
OGA: One Grung Above, an Extra Life fundraiser from WotC
PotA: Princes of the Apocalypse, Appendix A: Genasi
PS:ZEN: Plane Shift: Zendikar, Races of Zendikar at p. 7
PS:INN: Plane Shift: Innistrad, Life on Innistrad at p. 7
PS:KLD: Plane Shift: Kaladesh, Races of Kaladesh at p. 15
PS:AKH: Plane Shift Amonkhet, Races of Amonkhet at p. 12
Note that Plane Shift occupies a strange shade-of-grey space: it's "compatible with" D&D, published by WotC, but written by the Magic: the Gathering team instead of the D&D team (though the author of all of them was a former D&D team member). Notably, it comes with a disclaimer substantially similar to the one provided with UA articles:
The game mechanics in this supplement are usable in your D&D campaign but are not fully tempered by playtests and design iterations. For these reasons, material in this supplement is not legal in D&D Organized Play events.
SCAG: Sword Coast Adventurer's Guide, Chapter 3: Races of the Realms
TP: The Tortle Package, an Extra Life fundraiser from WotC
UA: Unearthed Arcana articles, link and name specific article when listing
UA articles are presented on WotC's website with the following notice:
You can think of the material presented in this series as similar to the first wave of the fifth edition playtest. These game mechanics are in draft form, usable in your campaign but not fully tempered by playtests and design iterations. They are not officially part of the game. For these reasons, material in this column is not legal in D&D Organized Play events.
VOLO: Volo's Guide to Monsters, Chapter 2: Character Races
WGtE: Wayfinder's Guide to Eberron, Chapter 3: Races of Eberron
E:RftLW: Eberron: Rising from the Last War, Chapter 1: Character Creation
Note that Wayfinder's Guide to Eberron and Eberron: Rising from the Last War now redundantly feature most of the same new races, though the latter reprints the goblin, bugbear, and hobgoblin races, and includes a new version of the orc race. WGtE was originally published as a "living document", and was later updated with the versions of the included races as they appear in E:RftLW.
EGtW: Explorer's Guide to Wildemount, Chapter 4: Character Options, Races
Monster Manual, Hoard of the Dragon Queen, Rise of Tiamat, Tyranny of Dragons Player's Guide, Out of the Abyss, Rage of Demons Player's Guide, Curse of Strahd, Storm King's Thunder, Tales from the Yawning Portal, Xanathar's Guide to Everything, Waterdeep: Dragon Heist, and Dungeon of the Mad Mage all do not provide playable races. Tomb of Annihilation does provide one in its The Tortle Package charity supplement (the eponymous Tortle). (And Xanathar's Guide to Everything does provide racial feats, so those interested in racial options may want to take a gander at XGtE anyway.) Tasha's Cauldron of Everything contains a Custom Lineage option, which is not a race per se, but relevant to mention.
Races legal in Adventurers League play (subject to "+1 rule"):
- Aarakocra (EE, only with supporting campaign documentation, EGtW)
- Aasimar: Basic (DMG, only with supporting campaign documentation)
- Aasimar: Protector, Scourge, Fallen (VOLO, EGtW) - Not subject to the "+1 rule" when created new for DDAL Season 9, and gains a winged option upon reaching Tier 2.
- Bugbear (VOLO, E:RftLW, EGtW)
- Deep Gnome/Svirfneblin (EE, SCAG, MToF)
- Dragonborn (SRD, PHB)
- Dwarf: Mountain or Hill (BR, SRD only Hill, PHB)
- Dwarf: Duergar (SCAG, MToF)
- Elf: High, Wood, or Drow (BR, SRD only High, PHB)
- Elf: Eladrin, Sea Elf, or Shadar-kai (MToF)
- Firbolg (VOLO, EGtW)
- Genasi (PotA, EE, EE, EGtW)
- Gith: Githyanki or Githzerai (MToF)
- Gnome (SRD, PHB)
- Goblin (VOLO, GGR, E:RftLW, EGtW)
- Goliath (EE, VOLO, EGtW)
- Halfling: Lightfoot or Stout (BR, SRD only Lightfoot, PHB)
- Halfling: Ghostwise (SCAG)
- Half-Elf (SRD, PHB)
- Half-Elf: Variant (SCAG)
- Half-Orc (SRD, PHB)
- Hobgoblin (VOLO, E:RftLW, EGtW)
- Human: standard or variant (BR, SRD only standard, PHB)
- Kenku (VOLO, EGtW)
- Kobold (VOLO)
- Lizardfolk (VOLO)
- Orc (VOLO, EGtW)
- Tabaxi (VOLO, EGtW)
- Tiefling (SRD, PHB)
- Tiefling: Variant (Winged only with supporting campaign documentation, or upon reaching T2 when created new for DDAL Season 9) (SCAG)
- Tiefling: Bloodline Variants (MToF)
- Tortle (The Tortle Package, charity supplement to Tomb of Annihilation; counts as part of XGtE for AL PHB+1 rule purposes, EGtW)
- Triton (VOLO, MOoT [adds darkvision])
- Yuan-Ti Pureblood (VOLO)
All races published by WotC:
All of the above, plus:
- Aetherborn (PS:KLD)
- Aven: Ibis-Headed, Hawk-Headed (PS:AKH)
- Centaur (GGR, MOoT)
- Changeling: (E:RftLW, WGtE)
- Dwarf (PS:KLD)
- Elf: Tajuru, Joraga, Mul daya (PS:ZEN)
- Elf: Bishtahar and Tirahar, Vahadar (PS:KLD)
- Elf: Avariel, Grugach (UA: "Elf Subraces")
- Elf: Palid, Sea (EGtW)
- Goblin (PS:ZEN)
- Grung (OGA)
- Halfling: Lotusden (EGtW)
- Hollow One (EGtW)
- Human: standard or variant (BR, SRD only standard, PHB, PS:ZEN, PS:KLD, PS:AKH)
- Human: Gavony, Kessig, Nephalia, Stensia (PS:INN)
- Kalashtar (E:RftLW, WGtE)
- Khenra (PS:AKH)
- Kor (PS:ZEN)
- Leonin (MOoT)
- Locathah (LR)
- Loxodon (GGR)
- Merfolk (PS:ZEN)
- Minotaur (GGR, MOoT)
- Minotaur (PS:AKH)
- Naga (PS:AKH)
- Orc (Eberron) (E:RftLW)
- Revenant (UA: "Gothic Heroes"), actually a subrace that can be applied to human, dragonborn, or tiefling
- Satyr (MOoT)
- Shifter (E:RftLW, WGtE)
- Simic Hybrid (GGR)
- Tiefling: Infernal and Abyssal variants (UA: "That Old Black Magic")
- Tiefling: Subraces (UA: "Fiendish Options")
- Vampire (PS:ZEN)
- Vedalken (Originally in PS:KLD, revised in GGR)
- Verdan (AI)
- Viashino (UA: "Races of Ravnica")
- Warforged: (E:RftLW, WGtE)
Disclaimer: As always, consult your DM before playing one of these races: these races may not be for all players. Stop playing a race if you're not having fun doing so. Neither Wizards of the Coast nor RPG.SE are responsible for anything you do while playing one of these races. Please roll responsibly.
Best Answer
Current as of AL Player's Guide v11.0.
The Adventurers League Player's Guide covers what is a legal DDAL resource. From the AL Player's Guide v11.0:
Eligible sourcebooks containing backgrounds:
Official D&D Adventure Products
D&D Adventurer's League and Guild Adept Products
Premier Organizer Products
Official Backgrounds from Sourcebooks
Also worth noting is that D&D Adventurer's League supports customizing a background, as per the PHB rules for doing so. While this allows for a custom selection of skill proficiency and tool/language proficiency, you're still restricted to equipment packages and background features as published.
Backgrounds from D&D adventures and other products
In addition, Baldur's Gate: Descent into Avernus contains alternate features for all 13 of the PHB backgrounds.
Additional Material
The information for older editions can be found here: