Today I happened to stumble upon (literally; not through that cursed webservice) one particular blog called, "Pagan Blog Prompts". It is a weekly-updated collection of prompts to encourage readers to expound upon various religious topics (under the assumption that a Pagan is reading and writing).
I found one prompt from January 2011 eye-catching: "Christian Paganism? Is it possible?"
I find this to be an utterly pointless question (with no insult to the author). I can't believe (ha) that anyone would have the audacity to call themselves both Christian and Pagan. While Christianity is indeed a derivative of Paganism, the two forms of belief have almost nothing in common. For one example, Christianity is monotheistic while Paganism is poly/pantheistic (depending on the practicioner's particular beliefs).
However, there is one thing that I'd like to point out about Christianity and Paganism that completely destroys the possibility of the so-called, "Pagan Christian". In Christianity, love is proclaimed and taught, yet there is hardly any love (this is, yes, a generalization). I can't tell you how many times I read or hear about Christians, especially Roman Catholics, who give to their church and not to some worthy cause, or who ignore their own doctrine and never perform acts of service to humanity. Almost all the Christians I know are just like this.
Pagans are much different, I find. Pagans do not always preach about love, yet they can be the most loving. (I take this from blogs and forum posts I read...I don't actually know a Pagan.) They are the ones who have a general love for nature (including humanity) as well as love for their gods.
It is because of this difference in level of love, that, I think, makes it impossible for "Pagan Christianity" to exist. There is a conflict of personality, of morality.
It's not that the beliefs are so different, because beliefs differ from person to person. It's that it is not possible to both love and not love in the same moment in time.