As for pro-life being a rightwing distortion, I don’t necessarily see how. It’s technically accurate.
The right does not support life as much as they are against abortion. Hence anti-abortion being more accurate.
Here’s another example - Republicans (in general) favor tax breaks that favor the rich while pulling government support from the poor. They care about making sure a fetus comes to term, but then don’t care at all what happens after it is born. That’s not pro-life either, that’s anti-abortion.