I don't buy the idea that there have never been any schisms or divisions within atheism (or that atheism even has a continuous history from ancient times to the present!)
Off the top of my head I can think of:
- Various ancient Greek philosophers who modern-day atheists "claim", yet these philosophers often had very different ideas from one another.
- Nontheistic believers in dharmic-type religions (who don't believe in any personal gods, but do believe in reincarnation, fate, "the universe", etc).
- Tondrakians (Armenian revolutionist movement, 9th-11th centuries; a small minority of them ended up embracing atheism).
- Enlightenment modernist/rationalist atheism, which valorizes science, reason, and progress.
- Nihilist atheists who believe there is no God and so we are ultimately all doomed and our existence is meaningless.
- Marxists and other reductionists who see all religion through the lens of politics and/or economics.
- Postmodernists for whom all truth and falsity (including the existence or nonexistence of deities) are inherently subjective.
- "Atheism Plus"/SJW atheists (atheists who also promote feminism and anti-racism as core values for atheists).
- "Red Pill" atheism (atheists who embrace racism and sexism, are explicitly opposed to Atheism Plus, and often associated with the neoreactionary movement and eugenics).
- Anti-theists (people who seem more intent on tearing down a particular religion--sometimes Christianity, less often Islam--than on building up atheism).
- Christian Atheists and Jewish Atheists who believe their respective religious traditions need to move beyond belief in God and will be better off for having done so.
- The Sunday Assembly, who don't claim to be Christian but do attempt to emulate the appealing aspects of evangelical churches.
- Atheist Satanists, who enjoy LARPing as devil worshippers but don't believe the devil (or God) actually exists.
- Transhumanist atheists, who don't believe in God but believe we might someday become gods (or godlike, at least).
- Panspermists, who believe that God didn't bring life to Earth, but aliens did, and one day they will return to "save" us. Raël, anyone?
And then of course there are also divisions about other cosmic-scale matters. The Big Bang Theory
depicted a relationship between Leonard and Leslie that went sour once they discovered that he prefers string theory and she prefers loop quantum gravity, and she ended up asking "How are we going to raise the children?" An obvious parody of religious disputes, but also goes to show that science itself has a lot of "camps" in it that themselves mirror religious divisions and are more a matter of leaps of faith than anything else.
And much as with Christianity, the borders between atheism and non-atheism are porous and not everyone (atheist or not) would agree that all of the above schools of thought are truly "atheist". And you have individual people who sometimes seem to sit on the fence between factions (e.g. Richard Dawkins, who's not quite Red Pill, but definitely not Atheism Plus).