Lets see, amongst the poor, blue collar workers (doing manual labour) tend to be more conservative. Amongst the wealthy, feelings of entitlement are correlated with time to go to the gym. Evolutionary psychologist: if you keep publishing nonsense like no one will take your field seriously.
FTA: "These associations remained significant even once the researchers controlled for political party." This seems to rule out the correlation coming from manual labor being associated with conservatism.
The headline was "Men's Biceps Predict Their Political Ideologies" you can't rule out political idealogical in a study about political Ideology. There is a spectrum of belief within political parties which explains why the association remained.