On the surface, they have Scroll and Key and Wolf's Head, but there was at least some civil business going on among the three. I wouldn't consider the rivalry any more serious that opposing collegiate football teams. Although, I could be wrong.

Skull and Bones is above political affiliations for the most part. They own the spread.
Members in the group I got stuck tagging along with were essentially given "horses" (politicians) to keep control of, and those ran the gambit - Republican, Democrat, Independents, etc. I got the feeling those who had more power and money were given Dems and Republicans to run, while the more annoying members got the independents - group hierarchy stuff. Republicans may have had slightly more control of themselves in some cases (Bush Sr) but that may be a personality thing. Some people are harder to ride.

I nearly lost my mind when it looked like Bernie might have a chance because I knew who was running him and how screwed up their methods are, and if you think the world has been bad, you don't even know how much worse it would have gotten.