Religion and empathy were main motivators drawing people to the Abolitionist cause.
Certain religious groups in particular (though anti-slavery sentiments cut across all faiths and denominations), such as the Methodists and Quakers, were vocal and organized in their opposition to slavery, seeing it as a cruel and evil system that violated God's laws. They, therefore, opposed slavery on the grounds of religious conviction. It should be noted, however, that even these groups were split: some Quaker slave owners left the faith after Quakerism banned slave owning in 1773, and as tensions rose in the build-up to the Civil War, some Methodist congregations split up, with abolitionist Methodists forming "free" Methodist churches near Methodist churches that would not speak out against slavery.
Empathy—the ability to put yourself in another's shoes—also motivated abolitionism. In this case, it is instructive to look at individual cases. For example, John Woolman, the Quaker who almost singlehandedly convinced all the Quakers in America to divest of slaves, first felt religious qualms about writing a bill of sale for a black woman to be sold. This general religious unease, however, developed into a strong sense of identification with slaves themselves. "There but for the grace of God go I" was Woolman's thought, for he accepted slaves as fully human, just like himself. He was a person who was sometimes sickly, and wondered he how he would fare under a healthy master who interpreted his ill health as laziness. Would he be beaten or killed? What would it be like to be a slave? It seemed oppressive as he saw the degraded way Quaker slaveowners in states like Maryland treated their human property. The question became even more real for him as he contemplated a Quaker trip to evangelize to the Indians. The Indians he was going to visit were very angry at whites at that moment, and some were capturing and enslaving them, which naturally made Woolman worried. It was easy for him to see how horrible it was to be a slave and not to want to have anybody else suffer that fate.
Harriet Beecher Stowe is a similar case. She saw slavery directly and was horrified by it. As a young mother contemplating her own children, it tore at her that a slave child as young as four could be sold away from their mother in some states. She thought about how she would feel if her own young children were ripped from her arms and sold to people who didn't care about them. These feelings of empathy, along with distress at a political situation that didn't seem to be improving, made her speak out in her influential novel Uncle Tom's Cabin.