The only thing you are telling me is that it is wrong because you decided it is wrong morally, or because most people decided it is wrong.
The only thing we can safely assume out of that is that it is your subjective judgement of value. Mine too in that case, but not necessarily an objective one.
The same goes with your slavery example, believing it is "okay" doesn't make it right indeed, but also doesn't make it wrong objectively. Especially since right and wrong are not objective values by definition...
As Publius pointed above, I don't believe in objectivism, as it is highly pretentious in its core premises. The simple fact that you take it for granted because "it took America a long time to figure it out" doesn't mean it is right or wrong. It just means that America decided it was wrong morally, which I agree with personally, but that doesn't make it more objective.
I could find countless explanations as to why people might believe differently for everyone of your examples.
I may believe that some things are wrong morally, but I have the honesty to say that it's just my view and political beliefs, not an universal constant.
Out of curiosity, do you believe in God ?
I'd answer that with another question (which is usually bad form), but just because I can come up with a reason to justify it, does that make it morally ambiguous or subjective? In that example, and sticking to the latter question, you could say that it's totally fine to kill someone who believes in abortion. That could be your belief, and others could find that wrong, but you could say it is definitively what you believe and you have decided that you will drive a pickup truck laden with explosives into an abortion clinic and level the block.
I don't think we'd find that idea shocking because of a sense of moral comparativism. The explanation for why that isn't right doesn't begin, "I know you believe this is right, but you're at this point outnumbered by those of us who believe otherwise. And in this culture, we try not to drive the explosive-filled trucks into establishments full of people we have political disagreements with."
I'm pretty sure the reason, for all of us, is that it's probably objectively, undeniably wrong to drive trucks full of explosives into any kind of civic structure in order to kill everyone. I don't think, in especially this extreme example, that any of us would have any problem saying, "This is definitely wrong, and if you believe this is the right way to handle this situation, there's something wrong with you." There's a point where we go beyond comparative ethics and into the realm of things being unacceptable anywhere for any reason.
Still, there are people out there who believe that's fine. I don't have a problem saying that the reason they're wrong, whatever they believe about abortion, has nothing to do with culture. If it's fine to drive a truck into an abortion clinic, it's fine to drive one into a church during mass for precisely the same reason. And both things are wrong, for precisely the same reason.
On the religious question, yes and no. I do believe in God, but I'm pretty rabidly antiestablishmentarianist as far as religious organizations go. It's complicated and could take up a whole thread on its own, which I'm totally fine with doing. Suffice it to say, I don't think any kind of religious choice I'd make as far as my life goes is an objective one. I have a sort-of, quasi-religious reason to go to the free clinic to donate my time. I wouldn't say you people that don't are evil for not doing it; that's my choice to do so. I don't think the idea that killing people is generally a bad thing is at all limited to religion, despite what a lot of people might say. Religion isn't the best way to judge objective good and evil, common sense and logic goes a longer way.
While I respect your opinion if you think that's true, I can't say I believe that. I can't imagine it will suddenly become acceptable in the eyes of all for me to skewer my neighbor alive and roast him on a spit as a sacrifice to my hearth goddess. It just doesn't make a lot of logical sense to say that something is objectively acceptable because I get a few people together who believe something else.
There have been a lot of horrible things that were driven largely by the unjust actions of a few people and the willful ignorance and inaction of a lot more people. Certainly a lot of American people were cast out of their jobs, exiled from their communities, and blacklisted from society for being "Communist" during the Cold War. While it was probably wrong of the McCarthyists to say that people should be essentially cast out of society for a peacefully-held political idea, it was a lot worse that the majority of Americans simply accepted it, whether they agreed or not.
In the end, I think you could say, with complete objectivity, that the massacres in Cambodia were bad and unnecessary, no matter if it was acceptable to that country's power structure or not. Not believing in mass killing as a method to garner political support, as an example, isn't really just a western/liberal thing. That homosexuality shouldn't be illegal is a pretty objective point, even though that sort of point is affiliated with our little block of the world. And that's not to say that we've got some kind of monopoly on good ideas. Limiting exorbitant interest on loans seems to be just now becoming a thing in our society, but that's been largely illegal in Islamic banking since the Middle Ages.
There seems to be an objective right and wrong in a lot of situations, it's just a matter of figuring out when that's true and when it's more an issue of personal preference that doesn't affect anyone else.
If you were to say that's there's a biological or anthropological impetus behind concepts of morality then I'd probably say there's same basis there. Most mammal species appear to have the instinct of not actively seeking to kill their own members and there seems to be evidence of it with humans - it's why a lot of modern militaries have training techniques to condition soldiers to override that instinct. However, while morality might have some biological basis it's still the product of rational thought and discussion that goes beyond innate instinct for me since we do have the process for the creation of ideas and their development.
I don't think chattel slavery was abolished as institution used by European colonial powers and in America due to some sudden moral epiphany of right and wrong that made it unconscionable. It became unconscionable because of the rise of the ideas and concepts such as liberalism, such as individual liberty, such as democracy, or the rights of man and the authors and people that promoted them until they became more widely accepted by society as well as historical events such as the French Revolution that gave fertile ground for those ideas to take root. England only abandoned slavery in places like Jamaica because of radical Whigs in Parliament who, in having accepted the concept of things like individual liberty or universal rights of men, fought to abolish it because it was inimical to their notion of morality and which apparently differed to that of conservatives that opposed it.
That initial impetus of classical liberalism and its philosophical and intellectual development over the centuries has more to do with modern morality in the west and what we consider right or wrong as Western societies. Those ideas are the product of continued development through debate and discussion to define what society comes to consider right or wrong. Racial equality, universal suffrage, gender equality, abolition of slavery, and a lot of things we probably take for granted in a western democratic society these days were the result of efforts to redefine what is, and isn't acceptable as moral standards.
I suppose for me I hold that there's probably certain biological and evolutionary instincts as social primates that humans have such as not killing each other, working together, altruism, empathy, or compassion that is probably as close as it gets to having some form of objective right or wrong. Beyond that, with morality itself, it isn't the product of some primal drive but the fact that we as a species have the capability for complex thought and it's just a set of ideas people and societies create. So no, I don't see morality as being objective but rather a particularly fragile and tenuous framework of memes that are developed and created over time and that need people to accept, maintain, and propagate as a society.
Because to be honest, if hypothetically, there was a collapse of modern society and all the collected works and thoughts that have permeated through and taken for granted today living in a liberal democracy, then I doubt later generations will have similar concepts of what we might think is generally moral or immoral.
I kind of think I take exception to a few things there, but not all. For one, I don't necessarily believe that just because we've conceived of something and that it's born completely from rationality that it doesn't actually exist, or that we invented it. It's a bit like saying that, because we noted how long it took to complete something, we invented time. Time's always existed and, though it's a bit more complicated than we originally thought, it was here a long time before us. It is, however, something humans conceive.
On the subject of historical movement, I honestly think it's moved in a relatively similar direction, even in very distant cultures. The idea of, over time, people becoming equal in rights and having a few inalienable expectations in life seems to be a pretty common theme that comes with enlightenment. We kind of take snapshots of history, but over time, even often without us having to do anything, as means improve, we tend towards a somewhat similar end. It certainly hasn't been constant or consistent throughout. The Greeks were talking about equality among all people when "people" still meant Athenian, landowning, male citizens. It's sort of a general thrust.
I do agree that there's a lot of baggage we take with us. Democracy is a practical method of governance, but it isn't objectively the right way to do things. If we did have to hit the reset button as a society, that is one of the things I might see changing. However, I think the idea we shouldn't kill other people, for one, would resurface. So would equality as a fundamental human right, eventually. Over time, it might be different, but there would be common themes that we would understand to be universally good ways to evolve a society.
I suppose people have a fairly common idea that invading aliens from another place might have a drastically different way of life, but I imagine a few things will bind anyone that can unite intellectually to leave a planet and explore space. That's not something you can really do when you're trying desperately to kill everything in sight for your own personal gain; it just isn't feasible to get anything done as a society that way.
I think, maybe, morality is a very bloated word we attach some particular baggage to, but I think a central core of universal and obvious right and wrong exists. Outside of the obvious ones, what about lying? Try to imagine a society where it is wholly expected that if someone promises to do something, it is absolutely fine, hypothetically, if they don't do it. Could anything actually get done? You'd have to do everything on your own because you couldn't trust anyone else to do their part of the job, in fact you could expect just as well otherwise. You'd never advance as a society.
In ours, we have the benefit of the expectation of honesty, but can also invest a lot into it. When someone loves you and believes in you, and you intentionally betray them, I'd say that's objectively wrong and I'd be willing to argue that, by the nature of promises and honesty, that's objectively wrong. It'd be different if you promised nothing, but by promising and betraying, you have done objective wrong. I'm not sure there's a single society anywhere that has not had that as a moral element, even ones that didn't meet until relatively recently.
So I think it exists, I think it's bigger than people sometimes think. You just have to be careful about application, because it's, as you and others have intimated, easy to include something subjective in there because you feel strongly about it.