I'm sure some atheists could be convinced. The rule "all atheists will reject evidence of God" seems false. The rule "all atheists will accept evidence of God" also seems false. Life is more complicated than that. It depends on the atheist and on the evidence.
In this case, you're talking about Agnosticism rather than Atheism.
An agnostic and atheist both live their lives as though there is no god. Because it is equally meaningless to say "there might be a god" but describe no further characteristics of such an entity, akin to "their might be faires but you can't see them, hear them, touch them and they have no effect on the world in anyway".
People trying who insist on a difference are just emotively trying to find some perceived middle ground from which they will claim intellectual superiority.