In this story, the Handicapper General and her agents force handicaps upon citizens based upon their physical and mental abilities. If an individual is mentally gifted, that person is forced to wear a device that will distract and disrupt his/her thinking. Likewise, if a person is physically gifted, he/she is given physical handicaps. These handicaps are forced upon people in order to make everyone equal. If someone is beautiful, she/he is made to wear an ugly mask. In other words, the goal of this society is to have everyone as equal as possible in as many ways as possible. As a result, gifted people are deprived of using those gifts.
In contemporary society, there are plenty of examples of inequality which would not be applicable in making similar comparisons with this story. For example, in many instances/jobs, women do not earn the same wages as men. Racism is still a problem. And the wealth gap between the top 1% and the bottom 90% has never been greater. We have professional athletes who are clearly superior to most people in terms of athletic ability. We have scientists who build particle accelerators and are learning about the origins of the universe. Nothing is holding them back other than bureaucratic red tape.
But note that in the story, Harrison showcases his abilities on television. It stands to reason that Vonnegut is making a criticism of media, television, and/or popular culture. Similarly to how the handicaps mentally and physically numb people in this story, television does have the potential to numb our sensitivities to violence, starvation, poverty, racism, inequality, and even stories of hope. There are certainly programs that bring awareness to these issues but there are also programs that desensitize the populace as well. And if they numb us to the point that we don't care to think about them, we essentially become like the characters in the story. In other words, in this numb state, we behave as if everything is fine and everyone is equal. To be insensitive and thoughtless about real inequalities in the world is to behave as if everyone is equal. So, this is an example in contemporary society of how popular entertainment can numb our senses and sensibilities to the point where we stop paying attention to inequality. In a sense, when we stop paying attention to inequality, we mentally handicap ourselves.