The citizens go along with the rulers such as the Handicapper General because they live under a totalitarian government that forcibly exerts control over them.
In addition to this forcible control in which imprisonment or even execution is the penalty for non-compliance with the enforced equality of the citizenry, people have lost the capability of any independent thought or physical movement. For, they are required by law to wear mental-handicap radios in their ears that prohibit them "from taking unfair advantage of their brains." And, they are limited in physical advantages as they must be "burdened with sash weights and bags of birdshot." Therefore, any type of rebellion or independence of thought can be quelled by the enforcers.
When the beautiful and talented ballerina dances with Harrison Bergeron after they have shed some of their heavy handicaps, the citizenry continues to surrender to the sacrifices of civil rights so that it can be "safe" and "equal." However, a state in which equality is obtained only by the use of violence is no longer a free state.