Are Islam and Judaism also so precise? Eastern religions certainly don't follow some archaic book to a T and view it as some unquestionable truth.
Orthodox Judaism is very precise and does view the OT as unquestionable truth (at least as explained by the Talmud).
However, they do not believe to have the only path to Heaven. They believe Judaism is not just a religion, but also constitutes a "people", or a "race" (it is possible, but very difficult, to convert, and it is not encouraged), with special responsibilities from God. However, righteous people from all nations and races will also go to heaven.
This would basically mean keeping the Seven Laws of Noah, but there would be leeway for those, for example, who don't understand the severity of those laws.
One of the results of these beliefs is that a Jew has to do much more then a non-Jew to merit going to Heaven, since he has far more laws, and far greater responsibilities, although Jews are given slightly better "let-offs" for involuntary actions and lack of knowledge.