Chuchi Bergman can somehow identify carriers without a medical examination.
Fragile Y Syndrome is referred to some as the gift the creep left to humanity. For reasons unknown, the rate of male births plummeted in the years following G-Day. A thorough investigation found that most men of the modern day were producing only sperm which carried the X chromosome. Thus, they had lost the ability to produce male offspring.
Although rare, there are some men who were inexplicably still able to produce gametes with the Y chromosome. Men who still carried the Y chromosome were most often referred to as "carriers."
The organization Y Control was created to deal with the growing gender imbalance. Although they initially believed they could solve the problem by simply creating more males through genetic manipulation and then "releasing them into the wild," they learned that the solution was not so simple. "Lab males" generally did not develop the ability to produce Y chromosome sperm.
After this realization, it became Y Control's imperative to locate as many carriers as possible and "enlist" them in the goal of repopulation. It is well known that these men become virtual slaves to Y Control and forced to breed like livestock in Y Control's private facilities. Thus, being identified as a carrier is akin to a life sentence in prison.
That is why Gene Waterman fled from his job in Hiawatha after Dr. Swan determined that Ali Rugosa's unborn child was a boy. As mandated by law, Dr. Swan was forced to report Gene to Y Control as a carrier.