Been there, done that! I have an excellent instructor, who did a great job of shielding us (students) from the politics in the larger organization, but did make us aware of them when we started visiting other classes, so we would understand comments made to us by other students/instructors. When he left that organization and helped found a new one, I went with him, because I felt it was in the best interests of my students.
Like any other activity involving large numbers of people, dojang politics can really, truly, suck. If you are happy with the instruction you are receiving, and the politics in the larger organization don't affect you, I would continue to do research. If your instructor sidesteps the issue, chances are he doesn't want to get you, or himself, further involved. Not knowing your instructor, I can't say what his reaction would be, but I would suggest bringing up a specific question/issue rather than a broad concern, and asking about that, then work your way into larger concerns from there. If the organizational issues are so bad that you have moral concerns, discuss them with him and tell him why the issues concern you so much.
Whatever you decide, good luck to you in the future.