---"The disagreements between different schools of atheism would be no different from any other society."
Yes and no.
Yes I agree that a society being atheist hardly protects against schism and conflict.
But, again, lets not keep mixing up "atheist" with any particular view of society. Atheists hold different beliefs on the particulars of what a good society would look like. Remember, I am not one who says "If atheists ran the world, things would be better." As I don't think "atheism" per se supplies anything one could rely on for such propositions. One has to look at individual philosophies.
--- But it would seem like the absence of religion would allow for progress in many areas. "
Quite possible, so long as some other dogmatic thinking
does not take it's place to choke it off (see Stalin/Soviet Union for examples).
---"Or is religion absolutely necessary in terms of the glue of a culture?"
I don't know. I think it's still an open question. But it seems to me there is evidence that it is not necessary. For instance in small social groups such as my own (in which there seems to be no qualitative difference in my interactions with my atheist friends vs with my religious friends, whose views I don't share). And also on a macro scale - for instance there are heavily secular European nations that seem to be doing fine without appealing to religion to "hold things together."
Likewise, it's not like the preponderance of religion has held countries like the U.S.A. in harmony - there are great schisms, even among Christians.
It seems those religious countries with the most apparent "unity" are those under religious (virtually totalitarian) theocracy. And it doesn't seem either of us wants that, even at the expense of feeling "glued" together.
---"Can atheists only exist as minorities in countries with a strong religious identity? Many think Europe's move towards secularism, which should be something like the pinnacle of enlightenment from the atheist view, is the equivalent of cultural suicide."
Of course I would think someone who equates religion with culture would naturally conclude that throwing out the religion is throwing out the culture.
But that seems a rather narrow view of culture.