Re: Organizations- How important are they to you?
Although organizations can give credibility by association with a recognized shihan or standard of performance, credibility is something you gain in the community through your performance and behavior. Organizations serve a purpose by providing standard and somewhat consistency in grading expectations. They also serve as a connection to the aikikai-if you are so inclined.
As Mark noted, they also provide a teacher of sorts although one can belong to an organization and not really receive much instruction. Politics is an issue.
Personally, it does not affect me a lot as to how I train. I have always been one to seek out my training rather than let it come to me. However, it does somewhat affect my style in the sense of trying to learn what a shihan is doing with regards to technique. If I train with someone it is because I have sought the person's training so it helps me in that regards.
I have been in political organizations in the past and they definitely are not my cup of tea.