Earth has perfected organ transplant technology, so someone with access to transplants can live for centuries. The transplants are provided by disassembling criminals, because almost every crime is capital, and execution is by disassembly for transplant stock. Because every citizen considers himself or herself law-abiding, they believe they benefit from more transplant material... and would never become transplant material themselves. They think, "I'll never murder, or embezzle, or repeatedly violate traffic laws, so make 'em all capital crimes. Get rid of the undesirables, and a longer life for me."
Earth has a unified government and a world paramilitary police force: the ARM.
The ARM has three major duties: "mother hunts" (enforcing mandatory parenthood licensing, designed so that each normal adult is allowed to be the parent of two children only -- replacement rate reproduction only), suppressing dangerous technologies (in the hands of anyone but the ARM), and combating organlegging -- black market transplant providers who source their material by kidnapping and murder.
So, the presumption that you can't deny reproductive rights is just silly. You have reproductive rights, but if you're hunted down and killed for attempting to exercise them outside the constraints of a violently enforced law, what good are they?
Oddly, 22nd Century Earth of Niven's milieu isn't generally portrayed internally as a dystopia, because humanity has been conditioned into obedience and pacifism anyway. Most Earth citizens consider the status quo wonderful.