Many times, debates between Christians and self-described “atheists” become stagnant and unflinching, even before they really get started. How is this possible? Typically, the Christian will ask for some reasons for thinking that God does not exist. The atheist will then respond that he isn’t taking the position that God does not exist, but rather that he just lacks belief in God. While this is not the same as saying God does not exist, the Christian will insist that the atheist is using the term “atheism” incorrectly.
So what to do? I think the whole thing is a red herring. It’s just irrelevant how they use the term atheism as much as what they do with it. My suggestion: let them use “atheism” however they want. If they insist it means belief in dinosaur-aliens that are coming to kill us all, so be it. Just be sure you get that definition from them at the beginning and hold them to it.
So, for example, when an atheist infuses the term with the meaning of agnosticism, say something like, “OK, so you don’t know whether or not God exists. For all you know, he might or might not. Is that right?” If he says “No, that’s not right at all. I think, probably, God does not exist. I just don’t know for sure,” then you’ve put him right back in the position of having to support his belief that God does not exist (at least at some point; you still have to support your belief that he does exist). If he agrees with you, then you can proceed forward, knowing that he can’t appeal to evidences that do not affect your argument unless he is willing to support them as evidences against God’s existence (in which case he functions as an atheist).
The advantages of this approach are obvious. First, you won’t get bogged down in an irrelevant issue. Second, you will be able to discuss the parameters of the debate while engaging the debate itself. You will have no less than the debate partner’s agreement that he does not believe that God does not exist, and so cannot use that supposition without supporting it. Let them call themselves whatever they want. Don’t let them sidetrack you from the real issue.