Religious freedom is only one value of many values. There are other Republican values than creating a theocracy. For example, gun ownership, redistribution of wealth to the top, cutting funding for education, or suppression of minorities seem to be part of the ideology. An atheist may value some of those more than he worries about a theocracy. Such values are ingrained in the right wing ideology. Many exist more in perception than they do in reality. For example, "the Republican Party is fiscally conservative." But those values, real or perceived, carry weight.
Once again, the definition of atheist is one who doesn't believe in a god. Beyond that, many of us, liberal or conservative, have other values that we cherish more than our atheism. For me, environmental stewardship, national health care (although not specifically Obamacare), the wealthy sharing their proportion of the tax burden, and equal rights, all rank higher than my lack of religious beliefs.
Show me a Republican that demonstrates the he actually values these things, not just in his rhetoric, but in his actions, and I could vote for him.