Does the affiliation of a school affect you personally and how you train? Are you aware of political machinations going on? I am curious to hear the thoughts of the forum on this subject.
Organizations unquestionably do affect how people train, since if they did not there would be no point in belonging to them. Whether members of the dojo are aware of how they affect training is a different question. Obviously in any dojo the head instructor is going to have the largest impact on the type of training that occurs there, especially since in most dojos there is not much room to do things differently from how that person does them (or says to do them, which might not always be the same thing).
So then the questions are how and how much are these instructors influenced by the organizations to which they belong and how much are the students there aware of this influence. I'd say the answers to both of these questions vary from organization to organization, but generally it is in the interest of organizations to engender as much awareness as possible of the organization within its member dojos.