These sorts of discussions always go downhill because they very quickly turn into defending (and attacking) people as if their identity is inextricably linked to their wealth, which means that policy discussions are read (and sometimes written) as personal attacks. Can we do better than that, please?
I don't see a claim that any of these folks are bad people for their money. Gates, for instance, is doing extraordinary good in the form of philanthropy; it's a stretch to imagine that the "offensive economic inequality" is a judgment of his character (although you may be correct that parent's choice of word "offensive" was risky). There are grounds to criticize his richness based on the anti-competitive actions of Microsoft in the '90s, but his richness per se isn't valid grounds to condemn him.
What is to blame, what is "offensive," is a society that allows people to become fantastically wealthy like this. What would the harm for society be if, through whatever means, it was much more difficult to become this wealthy? Maybe it is high taxes on the ultra-rich, maybe it is an unwillingness to allow high CEO salaries, maybe it is a serious estate tax, etc. Is it really true that Gates, Zuckerberg, Page, Brin, etc. were motivated primarily by money to found Microsoft, Facebook, Google, etc.? If they had a 99% marginal tax rate once they have assets of $500M (on any form of gaining wealth), would we have a weaker Microsoft or Facebook or Google doing less good for the world because they wouldn't be working as hard? Would the good done to people on the lower end of the scale not outweigh any possible harm here? That seems hard to imagine.
And it is precisely because these people could be less rich that the comparison to racism feels ill-placed. A society biased against people of a particular race cannot make existing people cease being of that race, and preventing new people of that race would be grossly immoral. A society biased against billionaires can in good conscience make fewer people billionaires, and it can even prevent hereditary billionaires without any particular immorality (although I think most of the people on that list are self-made).