The mainstream churches played very little part in the abolition of slavery. Quite the contrary, in fact.
For example, the Church of England actually participated in slavery. Its Society for the Propagation of the Gospel in Foreign Parts owned sugar plantations in the West Indies, and it almost goes without saying that these were worked with slave labour.
Rather, it was the much-despised Quakers and Non-Conformists who led the fight to firstly end the slave trade, then eventually abolish slavery altogether. William Wilberforce, the key British politician in making the necessary legislative changes that abolished slavery, is described as being a "converted Evangelical Christian."
Back then Evangelical Christians were very much viewed as radicals, who threatened the established order of things. As well as being up against powerful vested interests (the slave trade was a highly profitable business, bringing great wealth to the port cities of London, Bristol and Liverpool), abolitionists such as Wilberforce also carried the social stigma of being "rather odd".
Not sure that they would have exactly fitted into the category of the "Religious Right" !