Temple judaism ended when the temple burned to the ground. They have reinvented themselves out of necessity but there is no reason to think that the cherry-picking activities of xtians are in any way superior to jewish scholarship on their own books.
I think the belief that an ancient set of books belongs to a certain group is faulty. Modern Jews are every bit as remote from the origins of these books as modern Christians. Both are interpreting the books according to their preconceptions. That Christian belief has diverged more notably from the source than the Jewish doesn't necessarily mean that it is 'wrong' or that it is not equally a successor to the originals.
The alternative belief is to think that someone is magically more competent to understand certain concepts because of their lineage. That is both silly and racist, and I will have none of it.
These books, as well as others, form the foundation of the western cultural tradition. Who can say where the influence of one set of books stops and starts? Who can say that one group is influenced by another, while return influence is not felt? There can be no true distinctions, except arbitrary ones.