Groups that have actually offered free voluntary sterilization procedures in impoverished areas were actually criticized as "mean spirited" and "racist" (I'm assuming since most impoverished areas have a high minority population).
There are several charities and government programs that will offer free hormonal birth control. So the meme claiming a lack of access is intellectually dishonest.
Conspiracy theory alert: I think the push towards not just the legalization, but the acceptance of, or at least desensitization to, abortion is part of a longer term plan. If or when population controls become mandated, if most of the population accepts abortion as merely a common medical procedure (like vaccines) for the "good of society" forcing people to get them will receive far less of a backlash, if any at all, from the people.