One of the things that makes me feel a little out of touch with many other Christians is that, intellectually, I am a theist first, and a Catholic second. I proclaim Christ's resurrection, I believe in intellectual strength of the faith, the evidences, etc, but if tomorrow you dumped Christ's bones on a table, my Catholicism would go on the spot - yet my theism wouldn't be so much as shaken. Hell, most of my moral beliefs wouldn't be any worse for wear, nor my fundamental metaphysical beliefs.
But I get the impression that this is alien thinking for a lot of people - and I've seen 'Either Christ or atheism!' sentiments in the past. To me that is just beyond bizarre, a little like saying that if a particular economic theory turned out to be false, that not only would they give up that theory, but the very idea that this thing called an 'economy' exists.
I've run into atheists who were extremely touchy about this same point - guys who seemed to be closet deists, but called themselves atheists because they were anti-Christian. Or who would flat out concede the success or rationality of everything from the Five Ways to the Kalam argument, but would dig in their heels about 'Christ' in particular - as if the word 'atheist' kept much meaning once you've conceded that much ground.
This, I've long thought, is the fundamental reason for the problems of religious faith in the West. Even popular apologists like William Lane Craig seem to be a little hesitant to spend too much time talking about God, full stop, and want to move on to Christ as soon as possible - which has the effect of making it seem as if he never really started talking about God to begin with, but always Christ.