I think it's important to remember that the Bible is not a single book. In fact, many books in the Bible, such as Genesis, are already compendiums of passages. Even within Genesis, some of those passages are compendiums of fragments, such as Genesis 11 which begins with the Tower of Babel and moves on to an entirely different topic directly afterwards.
Even if we are looking at just the New Testament, the four gospels, as well as the writings attributed to Peter and Paul, each have their own idiosyncratic beliefs. In fact, John is really the only gospel that hints that Jesus is God, with the other gospels only positioning him as a prophet and the messiah. The gospels also mostly imply bodily resurrection on a new earth, whereas Paul implies a "spiritual" resurrection in Heaven after death.
So, the question becomes, is Christianity exclusive? Sometimes, sometimes not. In fact, Mark and Matthew seem to imply that Jesus was not trying to create a new religion at all but to reform Judaism, and therefore had little interest in expanding to gentiles. There's even advocacy for continuing to observe the Torah, which most Christians don't do now. Yet other passages can be taken to imply that Jesus shared a new covenant that sheds a deeper light on the Torah enough to essentially replace it.
Then there's the bigger, more relevant question. What does it mean, metaphysically, to say that people may only be saved through their faith in Jesus Christ?
Would it surprise you if I said that Orthodox and Catholic doctrine, which are the oldest surviving Christian denominations, actually interpret this to mean that those who have faith in God can be saved? Because, after all, Christ is God to them in their theologies.
So what if there is only one true God? Does that mean that other monotheistic/monist faiths are false, or are they worshiping the same God as the Christians, just with a different understanding of him? It depends entirely on your interpretation. An argument can be made either way.
Constantine, who played a major role in the survival of Christianity and its adoption by the Roman Empire, believed that Jesus Christ was equivalent to the pagan god, Sol Invictus. Christianity would continue to adapt various pagan deities as angels and saints as it spread, even attaching to local sky deities around the world and explaining that they are God to ease conversion, while at the same time presenting underworld deities as Satan. They did this in the belief that other cultures often knew of God and the devil, but didn't have the pure, true understanding that comes from Christianity.
They also sometimes treated foreign gods as demons masquerading as false gods, too, and I don't want to downplay that, but they still often believed other religions were working with genuine supernatural powers. It wasn't until Christianity became a dominant religion that the idea that none of these other gods ever had any power beyond superstition grew to popularity, and even then that happened parallel to rising witch hunts.
So I think saying that believing in Christianity means that you have to believe all other religions are wholly false is actually a very modern idea, but there's a roulette there as to whether Christians think your religion is worshiping God or the devil. Luckily, I think calling all other religions and denominations "Satanism" has begun to fall out of vogue, maybe partially helped by the rise of unabashed Satanists, Luciferians, and demonolators.
