The flaw here is that you ignore that capitalism is based on the notion of the private ownership of property for the sake of profit. This means that it leverages greed and selfishness for the sake of producing profit. The desire to have private property means one wants something that no one else can have. This desire to have something no one else can have, along with the desire to expand one's wealth by getting out more capital than one put into an economic transaction are manifestations of greed and selfishness. Selfishness increases hatred of others because one has the desire to have something that others cannot have. Although it is not possible to make everyone equal in the economic sense, there have been systems that are based more on the notions of sharing and social responsibility. Not only that but we can see that there is a correlation between the rise in the number hate groups in the U.S. and income inequality. Therefore, there is good reason to believe that capitalism has created an environment that has allowed hate to increase.
I am not entirely sure you understand what capitalism really is, and what our economic system really is.
One, we are not a pure capitalist economic system, and I would go so far as to argue we have not been a pure capitalist economic system any time in this nation's history going all the way back to our founding. Mixed model economics has been around for a long enough time to suggest all we are talking about is how far the lean is towards market economics or towards planned economics. We might have been close here and there, but I doubt we ever achieve a total government (at all levels) complete hands off system of economics. Even right after our independence.
Second, capitalism is not the first economic system that included the notion of private ownership of property, private participation in an economic model, the idea of debt or profit, or the idea of collection of monetary power and/or collection of precious metals as a source of wealth and/or collection of resources as a source of wealth. As an example, Feudalism predates Capitalism by centuries. Feudalism did truly exist, was widespread, was market controlling, taxed, and involves similar collections of wealth, property, profit, and aristocracy. Going back further we can cite as an example the economic system of the Roman Empire. A somewhat lean to market economics (in the sense of that period,) but strongly controlled by central government, taxed, backed by slavery (some hatred there) and expanded upon by conquest and implanted regional governorship. Or, more collections of wealth, property, profit, and aristocracy. Both of these examples that really did exist saw unequal distribution of economic reward, had plenty of poor (and slaves,) and neither was a kind period for humanity or was peaceful.
The truth is these example systems of economics all predate Capitalism and in some regards generated more social turmoil, war, and fallout from collapse than we have achieved using our mixed model economics. Another harsh truth, in the context you are talking about, the closest we have ever existed to pure market economics was mostly during the Industrial Revolution period. Mainly across European Nations and the US (as it existed at the time.) In a large way, without urbanization then capitalism would not have had the same impact. The key was handling socioeconomic reforms of manufacturing, agriculture, and manufacturing.
What you fail to acknowledge are the facts. Both prior to and after the closest this planet has ever come to pure market economics, looking all over the globe, and going in each direction all the way back to the earliest of human recording and up through right here today we have overwhelming example after example of collections of wealth, ownership of property, economic systems that created profit from goods and services, people that had way too much and plenty that went without, crime, war, hatred, social classes and plenty of socioeconomic forces keeping them, a difference in rewards from development and advancement, and overall... aristocracy.
It does not even matter if we are talking about a pure wealth based aristocracy, or a governmental aristocracy, or some hybrid of the two they all took one thing. An economic model one could take control of in some respect for the benefit of the few at the expense of others. Every objective review of history shows this. Hate or indifference has always been there even in more planned economic models, and we have so many examples it is conclusive. You have little evidence that we all of a sudden found something spectacular with Capitalism (that never really existed in a pure sense) that caused some massive jump in hatred.