We can begin to think about this by considering the earliest humans. Subsistence living, short lifespans, unimaginable conditions. If they didn't reproduce then none of us would be here.
So your question is about contemporary times. What has changed? I can think of two things.
* Overpopulation. If you think overpopulation is a problem then you would want to consider the question of when it's wrong to reproduce. For the record I believe and have argued on an unrelated thread that the real problem is underpopulation. So for me this wouldn't factor in. But if you think overpopulation is a concern, you'd want to consider that as a factor.
* Privilege. Modern life is expensive. It takes a lot of money just to be poor these days. If we are wealthy and we bring a child into the world, we can give it all the advantages. But if we are poor, we condemn our offspring to a lifetime of starting behind and falling further behind every day. Food not as good, schools not as good, social networks not as good, "voted least likely to succeed."
Now on the one hand that sounds like a sensible argument. But I'd argue it's elitist and frankly evil. The poor shouldn't reproduce. From there how far is it to the idea that we should just sterilize them if they can't control themselves. You're not the first to think of that.
No of course I know you didn't mean to think of that! I'm only following a "sensible sounding" idea to its actual logical conclusion. And I'm just putting forth the proposition that the value of a human life is not measured by material things; and that if our current world is the opposite, then we should strive to improve the world, not abort the poor. Or equivalently, declare that it's a moral wrong for the poor to have kids.
Now having said all this, I believe you are stuck with the overpopulation argument. People shouldn't have kids because there are too many people. I hold the opposite because I believe wealth comes from human capital, and our problems are how to get everyone organized.
We have plenty of resources in the world, but terrible distribution systems. In the great American depression farmers burned crops because the prevailing prices wouldn't pay the cost of getting the crops to market.
So no, I don't agree that shaming the poor about reproduction is a good political, social, or economic strategy. In the end I think there's a whiff of elitism in the question. The lotus eaters get to reproduce. A baby is a cost center, not a new human being. Can't afford to give a kid an upper middle class life? Kill yourself now.
A society that develops such an ethos is doomed.
Note: I am not accusing you of being a terrible person who wants to kill all the poor people. I'm exaggerating my rhetoric to make my points. Sometimes people take me the wrong way. People these days are way too literal IMO. But I do feel there is elitism at the core of the question of who should reproduce. The other side of argument is humanism. Every person is valuable. Not just the ones lucky enough to have been born to parents who practice assortative mating.
https://en.wikipedia.org/wiki/Assortative_mating (*)
Perhaps the problem isn't that poor people can't afford to give their kids a decent life. Perhaps the problem is that we've arranged our society such that reproducing is a luxury not financially available to most people. That your human worth is your financial worth. And what should we do about that?
(*) The Wiki article is about a general biological phenomenon. I was using the term assortative mating in the way I've heard it, where upscale attorneys marry upscale politicians, or Silicon Valley couples give birth to kids groomed to start their own company by the time they're 12.