Fox News host Greg Gutfeld is on top of the world right now, at least professionally. He co-hosts The Five, his network’s top-rated show that pulls in more than four million viewers every weeknight.

Kat Timpf got pregnant, got breast cancer, then got back to work on the political comedy show “Gutfeld!” — all as a culture war brews over ambition, motherhood and women’s health. Kat Timpf has been ...