That is false. Most abolitionists were inspired by their religious beliefs.
How is that possible when the Torah, the Quran and the Bible, with more than 100 comments on the topic, do not condemn slavery?
In 1866, a year after the American Civil War, and at a time when half the nations of the world had abolished the legal practice, the Catholic Pope advised his large flock that he found nothing in Divine Law (his Bible) opposed to the buying, selling or trading of slaves. That Pope was correct.
You have overlooked the simple fact that religious people are also humans, and like the rest of us, gifted with conscience. You jumped to the conclusion that they were inspired by their religious beliefs when it was their conscience that moved them as it did the non-religious..
Conscience is now moving us to give women and homosexuals equal treatment. You won't find support for those moral advances in the sacred texts either.