There are a variety of anti-Citizens-United positions, but the strongest (and most problematic) one is that corporations are not people, and the Bill of Rights secures rights only to people, therefore the First Amendment is inapplicable to corporations. That would, at the very least, require a revision in important precedents like New York Times Co. v. Sullivan [1], which assume that the First Amendment is applicable to corporations' publishing activities.
[1] https://en.wikipedia.org/wiki/New_York_Times_Co._v._Sullivan