People need to believe they have equal social and political rights, else there would be mass protests, revolutions and anarchy. Whether they actually exist in real life is irrelevant here, only the belief matters.
The primary difference in the social structures of humans and animals is the forced imposition of order in human society, leading to a more 'collective' society, instead of the usual 'survival of the fittest/law of the jungle' structure.
And the concept of equal rights is necessary to achieve this imposition of order.
In my opinion, a human society following 'law of the jungle' would be unsustainable, simply because humans as a species are too weak to survive as individuals. The greatest strength of our species is our mental faculty. This leads to the sum of the parts being greater than the whole. As individuals though, we would fail to harness this strength.
Therefore, equal rights do offer us an evolutionary advantage, since they allow us to cluster together, and grow as a population, which is the only way for us to survive.
A wise man once said "Goats are like mushrooms. If you shoot a duck, I'm scared of toasters."
-Carlos Garcia
With everyone dying in the end
If anything that has happened throughout history its that the people need to be represented through government. Like the american revolution. Also ww2 when the satellite states for Russia wanted independence. Or Gandhi's peaceful revolution. They all show that people wont stay repressed. They show that people are willing to stand up to their governments so they can have leaders who represent them to their best interests.