Believing in God and the divinity of Jesus is surely retty fundamental to being a Christian. People may like to consider themselves christian (small c) but that doesn't mean they are.
Ah! You've met a true Scotsman, then? The divinity of Jesus question being fundamental or not has a long history, via Arius, the Unitarians, the Christadelphians and present-day Jehovah's Witnesses (all these of course not believing Jesus to be divine). However, they have considered Jesus in some sense of supreme importance, so if they want to call themselves Christian, I for one don't care (especially if they're people of the stature of Albert Schweitzer, who certainly wouldn't fit your criteria). There are doctrinal anal-retentives in all camps.
As for believing in 'God' - that's such an indefinable can of worms, but I suppose believing in some sort of creative force might be a minimum, but the Sea of Faith people think otherwise, and who am I to gainsay them?