Ok, aside from the recent unpleasantness....
I think everyone's agreed that JREF is not an atheist organization in the sense that, say, The United Way is a charitable organization.
So w/ reference to the OP, no, it's shouldn't be part of the mission.
But I think we also agree that agnostics and atheists make up the majority of the membership.
And I believe remirol's point is that we should be careful about allowing that fact to lull us into a mindset of considering it a non-theist (to lump atheists and agnostics together) organization by default, in the same way that many Christians are quick to identify the USA as a "Christian nation" to the great irritation of many non-Christians.
But of course, the USA is in fact a Christian nation in terms of demographics and culture, and there's the rub.
But there's something more here because, of course, non-Christians, as well as thoughtful Christians, can point to the Constitution and find language expressly prohibiting a state religion. So there's nothing about being American which should inevitably lead one to be a Christian.
But what's simmering under the surface at JREF, and I believe in the wider skeptical community (loose as it may be), is a sporadic debate over the issue of whether skepticism / critical thinking, when followed to its logical end, actually does lead one to be an agnostic or atheist.
And that's why I engaged remirol's assertions regarding the (un-)disprovability of God. Because if it's true that God cannot be disproven, but might someday be proven, then agnosticism and perhaps some forms of theism are compatible with skepticism / critical thinking.