Wizkids Rules!

While Black Adam is active, when a character die is KO'd, if it isn't a Sidekick die, return it to its card unless its owner takes 1 damage.

Are characters with the Ally keyword exempt from Black Adam's ability since they are considered sidekicks in the field or once KO'd they are no longer considered sidekicks?

Black Adam’s ability checks the game state after the KO has occurred. So, the KO’d Ally Character die would be in the Prep Area (unless otherwise stated, maybe the Used Pile) and is no longer a Sidekick Character die. Therefore, the Ally Character die will not benefit from Black Adam's exempting text and is returned to its card.