Some people work very effectively with a very clean desk and others work just as effectively only top of a cluttered garbage pile. Your preferences are your own, and people naturally get defensive if you try to get them to behave in a manner other than what they choose.

What to do is obvious once you get the above point. You do your own GTD thing, get agreements from others about what their work looks like, when it will be delivered, and what the quality expectation is, and then you just hold people to that commitment. Of course, if your going to hold others to their agreements you need to be near flawless honoring your end because everyone is a hypocrite, quick to remember the broken agreement of others and equally quick to forget their own failures.

Since over time actions speak at least as loudly as works, if you GTD your world, honor your agreements, and hold others accountable, you'll compel them to getting things done even if they never read GTD.