The revision that shows a tone that is judgmental toward women is:
"The path to management is full of obstacles for women. News organizations prefer to hire journalists from “hard” beats, which require travel and irregular hours. These demands can be too much for primary child caretakers, who are women in the majority of American households."
This version implies that the demands of these jobs are excessive for women, positioning them in a way that may suggest a judgment on their capacity to handle such responsibilities due to their primary caregiving roles.