So I pierced together the following backstory/information about the Wildcard gang from various Youtube videos on them on Youtube.

First, there is no "Wildcard Gang". At least as the game promotes it.

Once upon a time there was a criminal duo known as Wildcard and Ace, who is a female version of Wildcard though her costume has a hoodie and her ballistic mask more generic markings. Ace and Wildcard were BFFS but they had a falling out and now they are rivals.

As for the "Wildcard gang"; the dimensional rift in time/space that is part of the game's backstory, somehow destroyed Wildcard's mind and splintered his mind into four different personalities; who's dominance is indicated by the mask he's wearing.