if you join an organization claiming
>independence from a political party,
>are you not contradicting yourself?

in the current state of politrical affairs, the term "independent" can mean either independance from political parties, or independance from the choices on the registration in your state. When I first registered in PA, you could register as Republican, Democrat or Libertarian. I chose "Not Affiliated" because I did not affiliate with any of the three.

The term Independant is spoken from a point of view of dominant paragdigm politicians who see people as a function of enemy, ally or undecided. Although it lexically implies avoiding parties, in the context of today, it really means "none of the above"