Is historical accuracy a necessary component of religious belief? Fundamentalist Christians and Muslims would certainly argue that it is. I would argue that the teachings of most religions that apply to everyday behavior, to relations among people and communities, do not bear an inseparable link to divine guidance. In fact, the rules of everyday behavior do not vary much from one religion to another. The so-called Golden Rule can be found in most faiths, and even outside them in secular teachings. Outside of the Sabbath and "Don't worship other gods", the Ten Commandments are pretty much good common sense rules for how people should demonstrate basic respect for each other. Most of what is in the Koran, other than all the circular logic about how the Koran is revelation because God revealed it, and the conquer the infidels stuff, is good solid advice on how to be a responsible adult. Outside of those two Abrahamic faiths the stories of the gods and heroes are, as far as I know, not taken seriously as historical fact; the god and heroes may or may not have literally existed, but their historicity isn't the point, the lesson that the stories are telling is the point. But when we get to Christianity and Islam, somehow the literal, physical, verifiable, historical accuracy becomes the point. When so much weight is put upon the truth that Jesus or Mohammed existed, or that the Koran or Paul's epistles were divinely inspired, the emphasis switches from how one should act to what one should believe. If one takes the teachings in the Christian Gospels at face value, then it really makes no difference whether the Jesus mentioned therein was an historical figure, an invented character, a distortion based on a real person, or an amalgam of several different people, because the teachings in the Gospels stand or fall on their own logic and practicability, without reference to who promulgated them. One very common logical fallacy is appeal to authority - which is saying that just because "an authority" said it, then it must be true. Jesus, if the accounts are true, is the authority, he is the son of God, so what he says must be true, so any logic, or self-evident truth must now be subordinated to the reign of the authority. But if what is contained in a holy book is true, then what is said will still be true, no matter who said it and who wrote it down. Within Christian belief, where we run into problems is the doctrine, promulgated in the Pauline epistles, that it was Jesus' death, resurrection, ascension bodily into heaven and future return that is most important, pushing the moral and behavioral teachings off to the side and making belief more important than action. In fact, the idea that it is "faith alone", as opposed to "works" that is at the core of Protestantism, initially put forth by Martin Luther. Interestingly, several, if not many, pagan traditions have stories of sacrificed gods killed and reborn. None seem to try to connect these characters to real historical figures and place the importance on the lesson, rather than attempt to prove that they are "true".
So, I suppose the answer is that it depends on what your religious beliefs consists of. If your faith is built on an appeal to authority and on the quasi-magical attributes of a specific human or demi-god, then it matters a lot. But if one is focusing on morals, ethics, behavior, community and relations among people, then no, it matters not in the least.