Politicians are a lot more subtle and conniving than to do something so overt. Nope, it would be much simpler. They would begin to place in fellow travelers into positions of leadership at high profile churches and in front of every TV camera. They would slowly start to preach a message of 'compassion' for victims of rape an incest and social justice. They would begin to paint everyone who doesn't want to 'help' them as bullies and not compassionate. They would make these 'compassionate' churches the mainstream and anyone who opposes abortion will be painted as radical extremists. It will be pushed in the media and pop culture. You know it is happening when you start to see the church become popular in the media again.
The only reason for stories of reeducation camps is to feed people's fear- which is a way to control them. The reality of how reeducation is done will be done right under most people's noses, to the cheering of the masses.