Is Christianity the sum of the actions and beliefs of its adherents or a set of actions and beliefs defined by the Bible? This question is closely related to those regarding the definition of a Christian that was also discussed on the meta site here and here.  While I consider that question answered and outside the scope of this site (as discussed in Meta), it seems that there is still room for this tangent.  Quite apart from what individuals are labeled as Christian, is Christianity the sum of the actions and beliefs of its adherents or a set of actions and beliefs defined by the Bible?



Background: I recently referred an acquaintance to an article describing differences between Jews and Christians.  I (converting to Judaism) said that I thought the article pointed out important differences between Christianity and Judaism.  He (a Christian) said that he thought the article pointed out the differences between some Christians and some Jews.  Obviously he is correct in his observation, but, by doing the latter, the article was (to my mind) also doing the former.
This question is very subjective as it appears you are trying to separate what Christianity is from what its adherents do, and that is very tricky.

Jesus had a vision of God's message that he understood very well.  Then he gave the pieces of the mosaic to his apostles, and taught some parts to his disciples.

They then tried to recreate the picture that Jesus understood.

So, they passed those pieces on to use in the form of writings, but many of these came from disciples of those Jesus taught.

So, we now have thousands of different groups each claiming to have reconstructed the picture, but each one is very different, as some will have put different ones in the center, and most will have some pieces left out of the image as unneeded.

So, when you ask what is Christianity, both can be seen as Christianity, there are the teachings, but how those are applied in the real-world shows whether the teachings are reasonable to follow, and so likely to be true.  If you teach a belief that no one can follow at all, then it is probably not a true teaching, but just a theory on how to live life.

So, in the US, we have Christian groups that teach hatred, and teach that treating those not of their particular faith as being less important, unless they can be converted.  

This would seem to fly in the face of Jesus' teachings of loving enemies more than ourselves (not something Jesus stated directly, but can be inferred), and being willing to die for those that persecute us.  But, these followers can seem to be happy with making this unreasonable loving part less important, or redefining it.

But, to an outsider, this is Christianity.  To those on the inside they may state it isn't, but if anyone group claims to be Christian then the entire teachings of Christ are judged by the actions of the claimants.

This is why Fulton Sheen stated that people don't hate Roman Catholicism, they hate what they think Roman Catholicism is.  People see something and may misinterpret, and so they hate this religion because of what they see, and what they may misunderstand, but to those within the Church they will see it differently and so not understand why people will judge the religion so harshly.  I am not trying to defend the RCC, but to use it as an example, btw.