Evidence really isn’t a function of a belief system. The evidence that the earth is not flat is wholly independent of the belief systems of those who may continue to argue the opposite.
There’s no evidence that unicorns exist, hence my “un-belief” in unicorns. There’s nothing religious about that position. There’s nothing religious about my atheism.
Contrary to your contention, there is indeed evidence for the existence of unicorns. Its just that most people do not find that evidence convincing. There is evidence that the world is round. More people find that convincing. The point is that the process whereby you find evidence convincing or not is certainly a value judgement on your part.
Atheists, naturally, assert that their judgement on whether evidence is substantive enough is based purely on reason and rationality. Apart from that being bloody insulting to everyone else, I dont believe it for a second. Human beings are creatures of reason and rationality, but we are also creatures of emotion and instinct, and they play as much of a part in the decision making process of atheists as anyone else, and certainly more than they fondly hope.