Atheism refers to the lack of god-belief, meaning that it does not require any more of someone than not believing in gods. In the United States, atheists are far more likely to vote for Democrats than they are to vote for Republicans; however, there is nothing inherent in the meaning of atheism that requires this to be the case. I suspect it is the case mostly because the Republican Party has explicitly embraced evangelical fundamentalist Christianity at least since the late 1970s. It is no secret that evangelical fundamentalist Christians regularly push things with which most atheists strongly disagree, so it makes sense that relatively few atheists would support a political party that aligns with them.
Briefly consider three issues on which the religious right (i.e., evangelical fundamentalist Christians who have aligned themselves with the Republican Party) has been rather vocal: women's rights (e.g., reproductive rights, gender equality) and LGBTQ rights (e.g., same-sex marriage, LGBT service in the military, discrimination by private businesses), and censorship (e.g., banning books, music, films, and other forms of creative expression deemed objectionable or blasphemous). Their rationale for the positions they take on these issues are nearly always couched in religious language.