"without violating the rights of another person who has nothing to do with it"

You mean the baby?

You talk in libertarian worldly fantasy language. That is not reality. Wake up. No Talmudic nonsense will be tolerated. Right and wrong is black and white. The Non-agression principle is designed to make you think you are free until another power commits aggression on you and fucks you in the ass for being a damn fool.

To answer your question, you can never stop people from having abortions. They can use evil methods like coat hangers and other satanic shit.

What you CAN do is block it so it's not a cultural norm and public funded way for child sacrifices to Mollach.

In the end, if you murder a baby, it's between you and God. Repent.