You said more about what you don't like about the Bible but you didn't really answer the question.
The Bible as a whole does teach equality and tolerance.
Is that the part where God encourages the slaughter of any but his chosen people or his worshipers? Or the part where certain duties are proscribed for women and not men or men but not women?
Half the big ten commandments (surely those were not rejected with the rest of the old testament?) have nothing to do with morality, but about stroking the ego of a purportedly omnipotent, omniscient being... and those commandments are placed ahead of those for murder and theft.
If you're going by things attributed to Jesus, then you're having to put up with massive contradictions between the Gospels. The same guy who sat down with whores and sinners also told his followers that in order to be holy they need to abandon their families to truly follow him, and smote a tree for not having fruit to give him.
There is a common, agreed-upon human morality. For society to function, we do not kill one another without extreme cause. We do not steal or cause deliberate harm to others. We act with charity when we possibly can. Those things have existed for as long as human civilization, and probably much longer. I suspect that every human society reaches the understanding of these principles, and that doing so has far less to do with religious belief and much more to do with allowing us to live in groups in the first place.