The problem isn't the Bible, the problem is with the fact that humans are not especially empathetic by nature. We generally put ourselves first, and then rank the social groups we're a part of based on how closely we associate with them. Usually family is first, then community (or tribes/clans/extended family groups), then we have things like organizations (businesses and clubs), race, nation, and finally species. But once you get outside of the immediate community, the others are all fairly abstract. The point is that we're all connected, but most of us don't have the ability to perceive it because it it's too far outside of our myopic empathetic sense.
For example, all human beings are related to each other. In a very real sense, we're all part of a giant extended family. But we can barely perceive the connections to our extended family/community. Once you get past that, it disappears into the "one, two, three, many" paradigm. So the artificial connections between us based on perceived differences (organization, race, and nation) seem more real to us than the actual physical connections we share as members of the same species.
Until we figure out how to make people empathize with each other as members of the same species, then we'll continue to be divided against ourselves. And while part of it is due to ancient superstitions used to explain some of those differences, much of it is due to uninformed, ignorant prejudice.