Nobody's stopping them, but it's still and irresponsible and terrible idea.
If you believe that poverty is truly outside of individual control, the situations are analogous.
Extra chromosomes don't come about due to unjust political choices being made on behalf of parts of the electorate.
Poverty is generally outside of the control of _those who suffer it_ largely because money brings power.
Those without money naturally have less.
Consider your views carefully, because at present they're definitely not worth reproducing.
If you are impoverished (and thus unable to meaningfully effect change in the system that impoverished you) it is irresponsible and bad to have children because the outcomes for those children will be bad.
You may decide that this state of affairs is bad, but that doesn't change the fact that it is still bad today to make an individual choice to have children in poverty.
This greatly trivialises the reality of poverty.
People aren't poor by choice; they're often poor through situations that are beyond their control.
To also suggest they're not allowed to have children because of these factors beyond their control is tantamount to an injustice.