Politically they align with the rich and the republicans in the US. They're not the team for the middle class or poor American.
I see them as politically the opposite of what you said. If you really want to stretch them having a "political identity", which I don't think American Major league sports teams have . They are in one of the most liberal states in America and their local fan base is compromised of registered democrats, often of non immigrant parent background, upper middle class, and lapsed/former Catholics religiously. When people talk about east coast liberal elites, the home base of both the patriots and Harvard falls into that. Democrats are not the party of the poor and middle class btw. A large part of the working class votes Republican, middle class is very split, and a lot of the super rich vote Dem.
If you are talking about Brady's and Belichik's views as proof of their republican ideology , that's a terrible way of judging teams . Even in soccer, there are plenty of players/managers/owners with differing views from their clubs rep. Breitner was a communist who played for Real Madrid, Abbiati is a fascist and he plays for the left wing Milan, De Rossi has right wing views and is a talisman for historically left wing Roma not Lazio, Zannetti talisman for right wing inter is a supporter of a Marxist rebel group in Mexico, rangers had a catholic captain once.....
Not that I think political affiliation with sports even really exists outside of soccer. It exists in soccer because of the uniquely well developed ultras culture that this sport has. If you don't have ultras it really doesn't make sense to say a sports team has an ideology. I'd say its getting less ideological now.Spain a previously very political soccer culture has recently launched an inquisition against ultras and most teams stadiums including Barca Real, and Bliboa are apolitical now and look like an average American sports stadiums.
), it is smart and we should be doing that too. 
