Nobody can truly determine if someone will be a good parent. The person who sets the terms is the government, and depending on the regime, what is enforced is inevitably going to be different. For example, I'm certain leftists would be concerned a far-right government would prevent homosexuals from adopting, or maybe prevent foreigners from having kids. Meanwhile, right-wing individuals may be concerned of that a left-wing government will prevent you from having kids for holding right wing views, or heck, in a communistic society, if you come from a rich family.
The reality is, these systems would have to be enforced by somebody, and can we truly say we'd be able to trust the authority to create a universal, politics-free law for who and who can't have children?
For example, I could argue that I don't think that the mentally ill - especially those with schizophrenia, psychopathy, or BPD should have children. However, I can already tell that will be considered 'sanist'.
Some people may say we shouldn't let felons have children. Then what does that say about the ability to rehabilitate?
It makes no sense. There shouldn't be prohibition on having children. That is a god-given right, so to speak.