It is irrelevant if there is "income inequality". The rational question to ask is "what is the quality of life of low income workers?" Who cares if some wealthy person is making a lot of money.. Why begrudge them their wealth? Where is the logic in that?
It is mostly accepted among economists that poor people are better off today than they were in the 1970s. Do you believe these economists are wrong? Good: That is an argument I'm happy to have with you- It is a relevant and rational argument. I suspect the economists are right, but I'm not 100% sure on this, either.
On the other hand, it's possible there are rich people that acquired their wealth through underhanded means. Again, if you think this is the case I'm happy to have a discussion on that topic. I think there are many cases where this has proven to be true. However, it isn't relevant in a discussion on the situation faced by low income people, because the welfare of the poor and rich are separate issues. They are not linked in any simple-minded fashion.
In summary, I think the recent fad of discussing "income inequality" is a shell game that mixes together several unrelated issues and clouds attempts at rational conversation. It is a tool people use to make dishonest ideological arguments.