It may seem to some that those don't belong together, and I would agree that they should not. Unfortunately, however, the Christian conservatives have a stranglehold on republican politics and a strong influence on many issues and how they are presented. Democracy doesn't exist without public opinion and polls have shown that atheism is unpopular in the USA.
There is significant misinformation about what it means for a person to be atheist. In particular, it's commonly asserted that atheists have no morals because morals come from god. First, morals do not come from god. Second, atheists do have morals even if different than those of Christians.
Morality is a social code that may be enforced by law or other social convention. Christian morals are based on the old testament and enhanced by the new testament including the teachings of Paul the misogynist and Jesus. Old testament law is based on the code of Hammurabi about 4 centuries before Moses. There are other social codes that predate the code of Hammurabi. Even if the law of Moses were considered independent of the code of Hammurabi, the fact that social laws existed long before it demonstrates that morality predated god's law and is not dependent on the god of the old testament.