the last western country to outlaw slavery
We fought the bloodiest war in our history (measured in terms of killing the largest percentage of our people) ending it.
Interesting that you qualify that statement with "western"; slavery was officially abolished in China in 1910, but still exists in some regions. It's also quite widespread in Africa.
The country that practiced segregation in living memory
Unlike, say, South Africa, or India (where to this day the Dalits (aka "Untouchables") are segregated:
Dalits are not allowed to drink from the same wells, attend the same temples, wear shoes in the presence of an upper caste, or drink from the same cups in tea stalls
Then there's the religious segregation in Bosnia-Herzegovina, Iran, Saudi Arabia (non-Muslims are forbidden to enter Mecca or Medina). I could go on, but I won't bother.
Call it "propaganda" if you want, but notice which direction the people illegally crossing our borders are going. Look at how the communist East Germany had to put up a wall with border guards under orders to shoot anyone trying to flee to the West (where US, UK, and French authorities permitted a goverment that respected the liberty of the people). If the reality of the liberty in Western Civilization in general, and in the US in particular, were that much worse than the "propaganda", there would be people going the other direction, and even some who came this way going back.
Of course we aren't perfect; no government is. But we are exceptional in the founding principles to which we aspire. Other people have taken notice of the practical value of those principles, and choose to emulate them.