You are right...
...but at the same time, if what is considered the highest authority around (with regards to Christianity) is interpreting the bible to allow for soldiers of God, and a place in heaven for those who kill Muslims and burn witches and blasphemers and heretics and the like, it suggests that the book they use as scripture can really be interpreted however they want it to be, and they can pick and choose parts to focus on, from old to new testament. It's much the same with Islam.
Christianity gained prominence in the world, not by separating radically from Judaism, as Christ's original teachings would have had it do. Christ wanted to take the power away from the Temple Priests and give it back to the people, much the same as Siddhartha wanted to take the power away from the Brahmin sect and give it back to the people in Buddhism's origins. Both religions gained prominence and many followers by compromising with the religions they were born out of. Christianity, through scripture and the later teachings of people like Paul, merged Christ's teachings with that of Judaism, to make it a more accessible and universal religion, not a religion of selfless ascetics, and it was much the same with how Buddhism developed. A religion of selfless ascetics, where each person has power of self-determination, and the choice of the path they take in following that religion, is a religion that will never grow, will barely survive, is monastic only. It's not a religion that the average person will take up. People don't want to be free to choose, they want to be told what to choose, told how to behave, told how to act. It's easier this way, it's easier to have a fixed path ahead of you. Hence the reason Christianity basically became Judaism 2.0
And this leaves it very open to interpretation for the Church authorities to push almost any agenda they desire.