I would turn this idea around: instead of barring certain people from reproducing (which has obvious issues), a society could require that all new parents take a course, go through counseling, or something like that, after which if they're deemed unfit to provide a healthy and safe environment the newborn would have to be adopted. This assumes it can be done to no economic cost to the new parents. It also assumes there are uncontroversial ways to determine fitness to parent. Basically a similar system to what most countries have in place for dealing with children in distress, but proactive rather than reactive. I'm sure there are issues with this idea as well, and the pragmatic way of trying to educate prospective parents is probably the best we can do, but it seems worth exploring.