It seems obvious that the answer is yes - low social mobility must have had at least something to do with the rise of Communism, and the Nazis also grew out of anger at wealth inequalities. Similarly, Donald Trump and Bernie Sanders (in different ways) have both recently attempted to gain power using the 'unfairness' of life as an argument for improving things. In Britain, the only reason the Labour Party exists, is because some people think that low-paid workers need some form of protection from their evil overlords.
I think there is an argument for having a somewhat balanced society. People who say (and they do) that footballers should not earn such large amounts do not understand how the economy works. Nor do they, presumably, consider that every Premier League footballer is automatically paying an obviously unfair 40% tax on most of their salary. I do not think it is wrong for a footballer to earn whatever a football club is willing to pay them. The football club is doing it because it can make money from Sky Sports et al, from prize money and from ticket sales, to make a profit on those players at those wages. Frankly, it is no-one else's business, how much money someone is worth.
But at the other end of the equation, there are people who will not earn a reasonable salary, and that is where the minimum wage (which I do not like in principle, but which I accept in practice) should come in. And in any case, if education is free, and if Social Services do their jobs properly, there's nothing in the way of any child achieving anything they set their mind to.
All these considerations, though, apply to a first world economy where no-one can exist in a situation where they do not have enough food and where, no-one should need to have no roof over their head. Education is free and no-one doubts its availability.
What about developing countries? Do we think equality of opportunity is as important there? What is equality of opportunity?
On an individual basis, I would argue that it is just as important in the developing world. But at the level of an economy, should an African government be concerned about equality of opportunity, or about ensuring universal education? Should it be spending time worrying about employment law and other legislation when its people live in real danger of not eating? I would argue: no. It's far more important for a country with those challenges to grow economically to a point where it can afford to resolve the inequalities that will inevitably arise.
When the country has stability, low infant mortality and economic freedom, then it can worry about whether some people are being unfairly treated by circumstances or the State.
Do you agree?
Washington Post: What's so special about equality of opportunity?
Individual differences vs. Structural inequality