Why can't the atheist be a Republican? It would have to depend on if they're tolerant or a fedora. If they're a fedora, they wouldn't win either party primary. An antitheist atheist would lose evangelical Republicans and minority Democrats.
It would be much harder to win a (Republican) primary I think. I also assume, that a vast majority of atheists are more liberal.
But to make it clear: I don't think of somebody who is totally against religion. Just someone who says: "I respect every religious person, but religion should be a personal issue. I, for myself, have decided to be an atheist".