Granted, let’s leave them aside for the moment and concentrate on those who have lived in Christian societies and rejected Christianity in favor of secular culture.
What has worked for me plenty of times in the past is to call them out on this in a charitable way. Richard Dawkins-esque arguments (since you mentioned him), are easily refuted. The idea that Christians believe in a Magician in the Sky is a ridiculously simplistic straw man fallacy on his part.
Second, science cannot disprove God. Only philosophy can do this. Science has as its end the physical universe… which God is not. Thus no science can disprove God. Furthermore, there is nothing within physics to suggest that anything within this universe causes itself to be. In fact, the very notion of the Big Bang gives credence to the First Cause/Unmoved Mover argument.
By showing an embrace of science, I share common ground with atheists. Of course, there are always a few who are as rigorously atheist as there are fundamentalist Christians. At a certain point, one must realize that no matter how the truth is presented, someone may not be open to truth.
I myself may have been a cradle Catholic, but I did my utmost to abandon my faith in college. I succeeded for about a year, but eventually had to open up to truth.
For these atheists (atheists influenced by Christianity, as you suggested), the approach that works the best is to meet them where they are. Primarily physics. There are so many philosophically inept physicists that it is so very easy to lay waste to the arguments of Dawkins, Hawking and Kraus. They may be decent physicists, but they make poor philosophers.
As you rightly said earlier, the theological approach will cause a shutdown. I think I understand your question here better, after reading back in the posts in this thread. Although admittedly you do have a number of posts about different discussions/topics.
Concerning whether grace is a good starting point, I find it is nearly impossible to determine this as some universal. Some atheists do appreciate theology. “Real” atheists appreciate philosophy more (in my experience). And most “anti-theists” respond well to the experience of the teacher. If they like you and see you passionate for your faith, it can make all the difference in the world.
I run a metaphysics class and I have some collegiate students who are not religious. Although they have many questions, they appreciate the depth of the subject. For those students, that is the only way I am able to address the need for grace (see my first post in response to you). They really got this part. Grace wasn’t an issue for them, since it follows from Thomistic metaphysics. The only real question is whether Thomistic metaphysics is true, but you can’t disprove it half-butted. It requires thought.
This is why I have respect for atheists like Terry Eagleton. They at least understand what it means to be an atheist. It is a belief system. Call a spade a spade. I appreciate the candor of this article:
lrb.co.uk/v28/n20/terry-eagleton/lunging-flailing-mispunching.
Honestly, I’m ok with a rational atheist… as long as they are rational and understand their opponents. This at least demonstrates the desire to find truth. This is something that popular physicists and scientists - Krauss, Hawking and Dawkins - fail at miserably. I point this out to my Christian atheists. If they don’t see the problem, usually a few other atheists do and point it out. Otherwise, it’s refutation of these points again!
I would like to respond to the rest of your responses, but I still have so little time. I do feel that I misunderstood part of your question earlier and hope that I did not seem callous. At any rate, I feel your questions are genuine and deserve proper response. And I do so ever enjoy a challenge! Good night.