LOL OP. Sorry, but i can't believe anyone is banning you from Facebook because how you play the game specifically. Perhaps more to do with what you have posted in those groups? Its one hell of an achievement to get banned from a variety of groups. You must have done something. At the end of the day, nobody on Facebook needs to know who you are in-game unless you announce it.
So, a group, set up by someone who has managed to get banned from all other groups? Well... sorry, that's not going to get me interested.
On the up side, if your group becomes popular, at least you will see things from the other side of the moderation fence.