Its set up similar to a terrorist network.
In general the large majority of Tea Partiers are built upon the notion of the "Contract From America" and its the closest to a universally held set of beliefs amongst all the various groups from a national to local level. There may be additions or tweaks here or there, but by and large those 10 things are universally held.
From there, you have over arching national groups, though even those aren't necessarily directly connected and consistent. They are less of direct figure heads as they are the strands that help connect the various local organizations. At this level the general core message remains relatively consistent across the board, with little variation and addition between the different groups.
As you move down from there into the smaller and more local tea parties you begin to see slightly more personal flavor on them. Tea Parties in Rhode Island may take a far more Libertarian appearance while ones in Arizona may look much more like a stereotypical Paleoconservative entity. Issues that are a bit more important to those local groups may begin to crop into their views or whats important to them based on the leadership or the membership at that lowest level. However, this individualizing tends to be something that doesn't translate up the chain or between various cells.
So individual localized Tea Parties act relatively independent, almost as unique entities, however are bound together by the commonlaities that they all share, generally through the connection to one or more of the national organizations, which are based off of the ideals of the Contract from America.
So it possible for a variety of localized Tea Parties to have a more social bend to them? Sure. There's also the possiblity for some to have absolutely zero social bend. Or a more miltaristic bend to them. Or hell a liberal social bend. But when talking about the organization as a whole, as the loose but connected entity that exists across the nation, one would need to look at what the binding message, purpose, and principles are and those are firmly and primarily rooted in Fiscal and Governmental conservative principles and issues.
To taking "football club" a step further. I really liked setting it up, and I manage to make it a nation wide thing with clubs springing up all over, mostly in cities with a football team, that is loosely tied together at a national level. At the national level we help facilitate clubs getting together for road teams to watch the game and argue with the home team or a forum where members can interact with each other. And other random national type things.
Now locally, clubs may differ a bit. The Football Club in Detroit may be less enthusiastic and small because, well, the Lions. The Football Club in Washington may have some members interested in checking out other sports but it isn't a big deal in the club because they live, eat, and breath Redskins. Meanwhile the Football Club in Atlanta may find it very important to do events where people can see Braves games as well because Baseball is important to their members even if its not directly important to the club. On the flip side, the Tennesse Football Club may have absolutely no care what so ever about Baseball because they don't have a team so their members are really not that interested in it.
So on the local level, the amount of additional interest or care shown to other sports may vary. But when you look at it as a whole, and from a macro level, the Football Club is still a club about Football, Football Fans, and watching Football. On a national level, it has no care nor thought about Baseball. It has no problems with its members liking baseball, or even some liking baseball just as much as football, but the Clubs focus as a whole is completely removed from any thoughts of Baseball.