The correct answer is D) "Those in power argued that if blacks were allowed a free choice of seating, white business would suffer."
The detail that best supports the central idea that many people oppose Branch Rickey's ideas was "Those in power argued that if blacks were allowed a free choice of seating, white business would suffer."
Let's remember that Branch Rickey was a white executive in the Major Baseball League, who, while working as a top executive of the Brooklyn Dodgers, hired Jackie Robinson, an extraordinary African American baseball player, the first to be part of the roster of a Major League baseball team. Of course, when he did so, he faced opposition form white people who felt threatened by the opening of the business to black fans.