UPDATE: Adventurers League changed the “+1 rule” in 2021.
An announcement from Q1 2021 gives the details. Basically, Adventurers League players may now simultaneously use any and all of the following sources when choosing player options like races, classes, subclasses, feats, spells, and backgrounds:
- Player’s Handbook
- Volo’s Guide to Monsters
- Xanathar’s Guide to Everything
- Mordenkainen’s Tome of Foes
- Tasha’s Cauldron of Everything
Other source books may also be available depending on the specifics of the campaign. The currently active campaigns (as of June 7, 2021) draw from subsets of the following list:
- Sword Coast Adventurer’s Guide
- Elemental Evil Player’s Companion
- Locathah Rising
- The Tortle Package
- Eberron: Rising from the Last War
Note that variants and optional rules must be explicitly allowed, so the variant Human, Half-Elf, and Tiefling races in these books may or may not be available. The same goes for the customized origins in Tasha’s. The best thing to do is to find and follow the character creation guidelines in the Adventurers League Player’s Guide specific to your campaign, which can be found here.
The revised rules have been implemented in these active guides:
However, the active Seasonal Campaign Player’s Guide (Plague of Ancients) remains the version from September 15, 2020. It’s likely to be updated when the next Seasonal Campaign begins.
The active Guidelines for Using TCOE in Adventurers League Play also predate the change, so must be revised.
Regarding the original question, Volo’s Guide to Monsters is on the list of source books available for all Adventurers League campaigns. Because goliaths are described therein, they’re allowed in Adventurers League play.
However, under the updated rules, choosing a goliath no longer prevents the use of character options from other allowed source books like Xanathar’s Guide to Everything.