In the anime it wasn't so much "Women's Rights" though that was probably mentioned once or twice. The problem was actually that Mars, where these robots were invented, was reliant on Earth immigration for their population stability. A Mars-First movement sought independence and believed (rightly, evidenced by the robot scandal itself) that extra viable wombs were necessary to divorce from Earth's inevitable political domination.

After a period of popularity for this political faction, there was a sudden reversal of policy where the new emphasis by the incoming administration was on Earth-Mars partnership and integration. This new political faction considered the existence of these robots (which had been secret, but the secret was getting blown open by a sensational serial murder case that the protagonists were investigating), to be a threat to 'peace' with Earth so they were being clandestinely hunted and destroyed.

Where "Women's Rights" may factor, is all of the discovered "Third" androids (the generation that could conceive) turned out were also famous in some way, because they had been made a little too well. They were top-selling authors, world-famous musicians, the most decorated police officer in the capitol city. Which heaped embarrassment on the exercise because it also started to question human adequacy when compared to them. It wasn't so much women's rights even then, though, it was humans vs robots.