Glowcat, you're assuming that an absolute morality both exists and is discoverable by man, and I don't think that that's possible.
Incorrect. Formalist morality may be a form of absolute but the form of morality I endorse is recently getting some attention in the form of Sam Harris's "The Moral Landscape." It is a very utilitarian perspective on morality. There are, of course, difficulties in establishing what exactly the ultimate goal should be, and by no means will I suggest that a single morality is universal for all possible values -- notably with regards to crazy violent people who enjoy murder and don't care about their own well-being -- but people in general have many shared goals that are intrinsic to being human.
Real morality is something that we have to think about, not write some unyielding principles in a book, tell people to listen, and call it a day.
This, however, is getting a bit too off-topic.
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I'd say that in virtually all cases, people do not derive their morality from their religion anyway. I mean... if the majority of, say, Christians did, when you point at one of the slavery verses the standard response would be "Yup! That's right!" rather than an explanation of why it's outdated. Religious and nonreligious alike people realise these laws are outdated and to some extent abhorrent because they have their own understanding of morality and why it's needed. I'd also think that this is why the basic instructions of most religions are quite similar - people have something of a natural understanding of a form of morality (possibly deriving from empathy).
I'd say two possible times when religion (not saying these two things are exclusive to deistic religions, though) can go wrong in terms of morality are:
1. When the entire thing is very firmly indoctrinated, causing that person to actually base their morality completely on it
2. If someone effectively cherry picks their religious ideas for support. This can be harmless, but in the case of bigots it can have the effect of reinforcing their views in a kindof echo chamber (you go in thinking gays are bad, you come out thinking that gays and bad and that God agrees).
I was actually thinking of slavery's abolition when I wrote that "extremely difficult" part about changing minds. People don't derive their entire morality from religion, no, but it is a major part in how they decide what is and what isn't moral. Take for instance the
Pew Poll about homosexual acceptance: more orthodox religious people who eschew secular values tend to have far greater rates of anti-homosexuality than people of a more secular influence.
I think that slavery may have only been overcome thanks to a competing set of values that spawned with the rise of Rationalism, not because human empathy finally decided to win out over long-held traditions at a moment that merely coincided with secular philosophy developments.