In this instance, you are flat out factually wrong. The American Anti-Slavery Society was founded in 1833 by William Lloyd Garrison and Arthur Tappan as an expressly non-religious institution to fight slavery. It included Calvinists (in various states of lapsedness) and Quakers but also atheists, Deists, and all manner of mid 19th century non-Christian seekers. It was one of many movements in the 1830s through 1850s that mixed abolitionism and feminism with criticism, often outright rejection, of Christian dogma.
Garrison's statements about religion in general and the Bible in particular make it clear he was
not a fan.
Likewise, Tom Paine was writing anti-slavery jeremiads 50 years earlier, well before the pulpit began to realize that the fact that owning human beings is sanctioned by scripture says a lot more about scripture than slavery.
There were Christian abolitionists, but abolitionism was by no means "inherently" Christian in any sense. The same people who have been gamely fighting to good fight against authoritarianism wrapped in Biblical raiment for all of history were doing it then, too.