Dont worry bout it. About two years ago you could not Wild Card an ATA. Now you can!

Quick question on Wild cards, If the Wild Card is assigned an ATA at the start of the game and they want to copy a friendly characters Mystics, can they still use the effects of the ATA while using Mystics or do they have to choose one or the other?

ATA are Additional Team Ability. Characters possess and use them in addition to any other TA they might have printed on their base or dial. The only thing you cannot do is using the same TA twice, one thru the ATA and one Thru standard TA mechanic (or thru any other effect). For example if you play a wildcard + Mystic, and there are other character using Thunderbolt ATA to use the Mystic TA, your character won't be able to wildcard Thunderbolt to use Mystic twice.
Hope that helps.