Hmmm I am kind of wondering, are you hinting at actual slavery in your opening post. Like with humans not having equal political rights and such?
Because I think being equally before the law and having equal political rights doesnt mean you are technically equal nor does it mean that 'inferior' men then suddenly should be put in places where they dont belong.
Our society is equal yet unequal. Every person has the right to vote, and he will be judged similar (should be at least) before the law as anyone else. That is what made him equal and I think that was what Lincoln was referring to. Still, we are unequal because obviously, one guy drives a Ferrari while the next guy needs to take the subway to get to work. We are unequal because one guy makes 10k a year and the other a 100k. We are unequal because one guy gets to be the president of the country while the other is only a janitor at a community college. That is how we decide the natural order. The guy who earns more or has more power, is more capable, smarter, stronger, etc then the guy who earns less. We measure the natural order by social status, wealth and power. And the reason why you get more out of life then someone else is because you were born with a predisposition towards intelligence, strength, and more importantly, you managed to make the most out of this comparative advantage over others. You maxed out your abilities or played on your strengths.
I like it this way. Differences are healthy, but everyone should have the chance to build out his strengths, even if they are minimal compared to others. And no need to see these persons as inferior. Even janitors play an important role in society.