You only need a level 40 character to unlock all Allied Races in Patch 10.1.5.
If you plan on rolling a new Allied Race character you should definitely wait until Fractures in Time. The latest content update for World of Warcraft lifts all requirements besides the level requirement. You will need at least 1 level 40 character to unlock all Allied Races.
Below, you can see the Zandalari Troll banner showing only the level requirement.