The 'Nine Traditions' currently only number eight, and one of those eight is quickly fading into the background. Those that remain are struggling with their own distrust and disagreements to maintain some level of unity as they try and take advantage of what may very well be their last chance to wrest the paradigm back away from the Order of Reason. The resurgence of interest in the occult and mysticism which currently exists is a golden opportunity and the Traditions are not going to stand by and not take advantage of it.
The Tradition mages of London are, luckily, some of the most liberal-minded and tolerant in the world, with two of the major covenants based specifically on the precept that all visions of the mystical are valid and, thus, all mystics should work together to see that the search for spiritual truth is not lost in this modern age. However, this is not to say that there aren't holdouts and reactionaries who, for any number of reasons, refuse to give an inch to accomodate their presumed allies. Particularly among the Hermetics and Choristers, both of which are famous for their tendency towards haughtiness and hubris and both of which have had troubled interaction with their fellow mystics in the past.
These competing elements show very prominantly in the attempts by the Traditions to influence humanity and in the politics of the local Tradition council, which tends to be a battleground whereby each representative spends more time looking out for the interests of the members of their Tradition (often by accumulating whatever power and influence they can) than cooperating and trying to discern ways to undermine the Order of Reason's iron grid on the modern world.