Yes, the northern abolitionist movement included people who were not Christians, but that really is beside the point. Wiliam Wilberforce in England was a Christian who almost a hundred years before the American Civil War spearheaded the British abolitionist movement. Christians here were encouraged by his success and worked very hard to abolish slavery all through the country. It's what led to our Civil War, you'll remember. They worked with many who were not
Christian, but they worked for it.
Tehy did so because, while the Bible acknowledges the existence of slavery, and when the Church was small and weak as it was in the days of Paul, it did what it could in the larger society to live as Christians in a culture they could not change. But when it came to their own, that they could change.
You mention the book of Philemon. A careful reading of it would see something already at work in the Church. Paul acknowledges the legal status of the runaway slave Onesimus, but, he says to Onesimus' owner, Philemon, in a letter accompanying the returning Onesimus,
8Therefore, although in Christ I could be bold and order you to do what you ought to do, 9yet I appeal to you on the basis of love. I then, as Paul"”an old man and now also a prisoner of Christ Jesus"” 10I appeal to you for my son Onesimus,[a] who became my son while I was in chains. 11Formerly he was useless to you, but now he has become useful both to you and to me.
12I am sending him"”who is my very heart"”back to you. 13I would have liked to keep him with me so that he could take your place in helping me while I am in chains for the gospel. 14But I did not want to do anything without your consent, so that any favor you do will be spontaneous and not forced. 15Perhaps the reason he was separated from you for a little while was that you might have him back for good"” 16no longer as a slave, but better than a slave, as a dear brother. He is very dear to me but even dearer to you, both as a man and as a brother in the Lord.
A slave as a brother? Find that in any Roman's thought. There is an interesting historical fact in the early church--there was a bishop named Onesimus.
It is Bible teaching like this that made the Church fight slavery. Not in spite of the Bible, but because of it.