I did some googling. John Tanton, eye doctor and environmentalist, Sierra Club, ZPG——this bears looking into. I don’t get the connection, what the purpose would be? How is illegal immigration connected to ZPG & eugenics?
It's a radical environmentalist view. The idea is that people are the problem. They believe in maintaining or reducing the US (and world) population. Therefore they support abortion and sterilization (of people they see as undesirables) as well as an end to immigration.
John Tanton, the founder of FAIR and other groups, started out in the radical environmental movement with the Sierra Club et al. They've been able to sucker a lot of conservatives who hold valid, reasonable views on strictly enforcing immigration law and controlling the border.