Almost all modern Christians passionately oppose slavery. Most, no doubt, oppose slavery more than they oppose gay marriage... especially the horrible race based slavery of the antebellum American South.
Most of the people I knew at my conservative congregation in Ohio opposed slavery by arguing that God intended for it to eventually be eradicated as part of his progressive agenda for the development of more just human interaction. They never seemed to recognize that if this same argument was used for any other doctrinal issue (like gay marriage) they would dismiss it outright as adding to God's word and revelation.
Because this argument is so popular it's worth exploring in more detail.
One of the problems with this reasoning is that it's never deployed outside the slavery question, and this is complicated by the lack of a good definition of slavery. Instead, they usually babble vaguely about the 'obvious' evil of racism, and the unjust nature of keeping people in bondage their whole lives.
Normally, no directly applicable scriptural references are made because of all the passages in the Bible that deal with the institution of slavery none of them condemn or even discourage it. On the contrary, many of them argue favorably towards it or even mandate it.
In fact, I would argue that contemporary American Christianity has no coherent theological thinking whatsoever when it comes to the issue of slavery. The sole exception perhaps being the most extreme forms of egalitarian Marxist Christianity which at least maintain a consistent progressive agenda regarding all of Christian theology.
Almost all Christian thinking regarding the issues of race and slavery in America are the result of often hysterical and always irrational fear driven reactions to the real or imagined sin of racism. What is racism? Well, it's whatever the leftist wing of society decides to define it as. So, in practice, Christian theology (if it can really be called that) regarding slavery is really a poorly thought out attempt to avoid accusations of racism, and what constitutes grounds for that accusation is constantly changing.
The primary problem regarding the idea that slavery evolved into a sin over the years is that if this is possible than it is conceivable that any number of arbitrary sins could simply evolve into existence. If this is possible then it would render Christianity a fluid and, ultimately, worthless moral guide.
If slavery is a sin than it is the only one never mentioned in the Bible, and if there are sins which aren't mentioned in the Bible than everyone is ruined on the day of judgment because God hid important stuff from us. No orthodox Christian thinker until the modern period has regarded slavery as wrong. Are they all guilty of doctrinal error?
The secondary problem with the argument that God progressively phased out slavery is that if Christians accept this then it only follows that God intends to phase out all unequal power structures. In other words, that he would be attempting to eliminate hierarchy and authority.
Is there really a difference between the slave/master relationship and the employee/boss relationship? Perhaps there is, but it is only a matter of degree not of substance. In politics, Christians run into the same problem. The feudal system that dominated the Middle Ages would have to be condemned because it mirrored slavery in all important aspects. Are monarchies to be done away with because the king has absolute, or near absolute, authority over the lives of his subjects? Are men not to have authority over their wives or even children?
The institution of slavery is merely one descriptor of a particular relationship among the hundreds that operate in human life on the principles of power, authority, and hierarchy. To declare slavery immoral is to declare that there is something inherently immoral about all these other relationships as well.
The only way to avoid this conclusion is to argue that race based slavery, like that seen in the American South, is somehow specially wrong. However, there doesn't seem to be any way of Biblically arguing this point because God specifically established race based slavery in Leviticus and made numerous socio-political decision based upon ethnicity and race. Ultimately, the question remains: why is basing a decision on race wrong? Is there any reason to believe that one has the moral obligation to ignore race when making decisions about social organization?
The modern obsession with being race neutral is simply unjustifiable. There is no reason to ignore race. God did not create different races and then force humanity to ignore them. Race is nothing more than extended family. People of the same race are always more closely related to someone of the same race than they are to someone of another race. God did not create family units and extended families and expect us to ignore them. The most obvious proof for this is God's special relationship with the extended family of Jacob.
There is no justifiable reason to view race based slavery as practiced in the American South as sinful? Of course, with all human relationships abuses lead to sin. Abusing one's slave has always been a sin just as abusing one's wife has been, but there is no reason to believe that the very institution of slavery has some how evolved into a sin in modern times.