There is significant income inequality of siblings with the exact same family background. One researcher found that the average annual earnings differential between brothers was about $28,000, compared with an earnings differential of $30,600 for men paired randomly.
That is, after controlling for sex, socio-economic status, religion, education opportunities, race, parental status, etc. (assuming those factors are usually the same for 2 brothers in the same family), there is significant income inequality of $28,000 between siblings within families, which is almost as much as the income inequality in the general population of males ($30,600).
And as Robin Hanson points out, there is also significant non-financial inequality, such as of popularity, respect, beauty, talent, ability, etc., and significant income inequality between the nations of a world, etc. that get very little attention, compared to the attention paid to income inequality among households in the U.S.