Cards can be greyed out for two reasons:
•        You currently do not have enough energy to play this card
•        There is already another presence of the same character in the battlefield (for example, another Kyle or another Stan etc, with a different theme or costume).
In the single-player Campaign, you cannot play any character that is already on the battlefield. That means, if I have a Randy in my hand, and there is already an enemy Randy in the battlefield (regardless of whether the other Randy is from a different theme or name), I cannot play Randy until that other Randy is dead.

In PVP Multiplayer, you can play any of the same characters that your opponent has in play, but you CANNOT play any same characters that you own on the battlefield. So, if you have one Cartman already in the battlefield and still alive, you cannot play another Cartman from your hand until it dies - so choose wisely!