freedom - the absence of or release from obligations
requires - impose an obligation on
"Freedom requires religion" literally means "The abscense of obligation imposes an obligation to religion."
For some reason, Republicans seem to think that people can only be free if they give up all of their freedom. For instance, Rudy Giuliani said:
"Freedom is about authority. Freedom is about the willingness of every single human being to cede to lawful authority a great deal of discretion about what you do."
discretion - freedom to act according to one's own judgment
authority - persons who exercise (administrative) control over others
Another obvious contradiction. Then again, Republicans have a long history of arguing that A is not A.