WASHINGTON — The Supreme Court will cut short its summer break in early September to hear a new argument in a momentous case that could transform the way political campaigns are conducted. The case, which arises from a minor political documentary called “Hillary: The Movie,” seemed an oddity when it was first argued in March. Just six months later, it has turned into a juggernaut with the potential to shatter a century-long understanding about the government’s ability to bar corporations from spending money to support political candidates. The case has also deepened a profound split among liberals, dividing those who...