Actually, Fox, in my opinion, the guidelines for what it means to be a part of the three monotheistic faiths(I'm thinking mainly of Christianity, since of course, that's the one I know most about) aren't as clear as you may think, or as clear as perhaps they once were. For example, yes, you must believe in Christ to be Christian, but what exactly does it mean to "believe in Christ"? Conservatives typically believe he is equal to God, the only true way to a positive afterlife, etc. To more moderate and liberal Christians, it's much less clear cut - they may believe in Christ in a way more similar to how Buddhists view the Buddha - as a wayshower, an example to follow, but not a deity. As a Gnostic, Christ plays a large role in my spirituality, and most modern-day Gnostics do in fact consider themselves Christians - however, our interpretation of Christianity is far different from the mainstream.
To remain semi-ontopic.... although I no longer consider myself Pagan, something I struggled with when I began practicing nature spirituality and spellwork was the more scientific aspect of my mind.... it took me awhile to realize that I didn't have to abandon my scientific mindset to believe in the power of energies and spellwork, etc.