The relationship of evolution and atheism can best be seen in the historical context.
When Darwin launched his Origin of the Species in 1859, it caused a shock wave in British and American society because it contradicted the Biblical account of divine creation. The stability and governance of both cultures were predicated on the rightness to rule by divine mandate (superior authorities) as the good book said. The Bible was believed to be inerrant; Darwin gave very good reason to believe otherwise.
If the Bible was wrong then the right to power was not divine. Shock horror! The forces of delinquency would be unleashed and the world order destabilized. Those allying themselves with the scientific theorem of Darwin would be castigated as atheists, a perjorative term with political and anti-religious overtones rather than a simple description of a person who does not recognize a god.
As already mentioned the reality has been that many who acknowledge the scientific soundness of evolution are not necessarily atheists but the reverse; to believe in creation and not in a god is an impossibility.