I knew it would be tricky placing you, as it will be for many of alternative ideologies (thank God there are no postmodern theorists on these forums).
Generally, I would suggest you go in the "Right" family, if you're interested in playing... if only because, out of the two, you would probably gain more joy from clobbering the Left family than from clobbering the Right family, although there are also at least some alignments with generally "right" theories. 
But as I said in the disclaimer, the categorization is inherently flawed (I never liked ideological categorizations anyway), but necessary to create this game without having 20 one-person families. It would be impossible to create families that perfectly fit with each individual's ideologies... so for this to work, I'm partially asking for people to make some compromise in order to advance a group... or at least to form coalitions with what one would consider the lesser of two evils.
As I stated, if a particular ideology has enough representatives that they can form a family outside the general "right/left" framework, they are more than welcome to do so, as long as they can mobilize enough people. I could definitely imagine a Libertarian group popping up in these forums. If we had more members, I could imagine splinter groups within each side of the "right" or "left," just as they exist in the real world.
The major issue in all of these would be finding 6 people who are willing to sign up for your side...
EDIT: Talked with the mods again, and apparently I misunderstood what they said. Apparently, I am allowed to play in the Politics ICC challenge. So I'll join either the Right group (if it needs more members toward the time to file final group numbers) or some alternative right/moderate/Justinian group, provided they find more members...
That being said, if I do participate, it would probably be advantageous for somebody from the Left and other families to step forward as leader early. There needs to be a designated leader for each individual family. However, in addition, if I am in one family and recruiting members for the other family, it would create the perception that I would be trying to stack the other family with bad players. Thus, if someone who does regularly play IC (you_fool, perhaps?) would step forward to lead their family, it would help ensure the credibility of this event.
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