Any birth suppression(even via propaganda) is going to favor some populations over others. It is eugenics even if you don't intend it to be.
I'm not saying the government should suppress births. People should do it themselves. By choice. I don't see how that ultimately makes it a race/class issue.
Different cultures have different levels that they will comply with your suggestion to forgoe children. Ironically, you'll end up with a population that's less compliant and pro-baby.
