The question seems odd... as if atheists are informed in all moral choices by atheism, or something.
I think it is you theists who confuse yourselves, because you live under the assumption (or pretend to do so on Sundays) that your theism informs everything you believe. Maybe it does, good for you. When you confuse yourself is to think atheists spend any amount of time thinking about atheism that even approaches the amount of time you spend thinking about theism. Most atheists just simply don't think or care about the concepts of theism or atheism at all, when forming their beliefs. So this atheism no more informs their view of the death penalty than does their opinion of 14th century poetry (that they also do not give a shit about or spend any effort on).
How man times did you think about Jesus today? Take that number, and that is right about how many more times you thought about Jesus today than an atheist thought about atheism today, on the average. That's kind of the thing with the default state of "non-belief".
For a comparison you can "feel", consider the number of times you thought about believing or not believing in unicorns today, and how this informed your decisions and beliefs.