Great analogy. Back in the 1980s two others and I were on the Montel Williams Show debating feminists about equal rights for men.
A feminist said, "Women have a right to their bodies."
I said, "Okay, then prostitution should be legal."
She said, "That's immoral."
I said, "Murdering babies is immoral too."
She said again, "Women have a right to their bodies."