What is genocide?
In the comments of both the question and the Africa Check answer, there was some discussion over the term "genocide". While it's true that there is not one scientifically agreed upon definition of the term, this is no cause for relativism. For one, there is the legal definition in the Genocide Convention adopted by the UN, which lists additional acts than just killing.
More importantly, there are a number of scientific definitions, which we can work with. Notable genocide researcher Barbara Harff proposes the following definition in Harff (2003):
Genocides and politicides are the promotion, execution, and/or implied
consent of sustained policies by governing elites or their agents—or,
in the case of civil war either of the contending authorities—that are
intended to destroy, in whole or part, a communal, political, or
politicized ethnic group.
This focus on the perpetrating group being government or government-like is a reoccurring element in the definitions of multiple other genocide researchers.
Is there a post-Apartheid genocide in SA, and, if so, is it targeting white people?
I have not seen that claim, if we define "genocide" as above. If that claims exists, someone should source it and try to find data on it. I assign this possibility a very low prior probability.
Okay, so the claim is not about genocide. But is there an unusually high number of hate crimes targeting white people?
I could not find any data on hate crimes for SA. If anyone can, this would be a valuable addition to this answer.
In light of this, we might simplify it to murder statistics. I was not able to find reliable data on this more recent than the one cited by John Strachan, so it would not be useful for me to just echo what was already said on this.
A most tacit approximation of empirical evidence
So far, so disappointing, because I was not able to find evidence either way (though of course, absence of evidence is weak evidence of absence). As to at least have some evidence, I'm going to use the South Africa Police Service's crime statistic for 2017/2018. It shows that there were 20336 murders in that timespan. Of those, only 2332 were assigned a specific motive in the statistic (I order by frequency):
- Gang-related: 973
- Mob justice: 849
- Taxi-related: 237
- Illicit mining: 94
- Police Officials: 85
- Farm murders: 62
- Political related: 32
Somewhat naively, I assume that the category "political related" is the best fit for "hate crime", but I might be entirely wrong on that point. If this were true, however, it would mean that out of 20336 murders, only 32 were identified as hate crimes, that would make a strapping 0.157%. Now even if we were to assume (without any grounds whatsoever) that all of those hate crimes were committed by black people on white people because of their race, this would not in any way, shape or form indicate anything even close to a widespread phenomenon.
Now I need to stress again that what I just presented was based on utterly insufficient empirical data, to the point where it's probably a sin to even speak of empirical analysis, and thus should be taken with heaps upon heaps of salt.
Edit: As proposed in the comments, I'm going to assume the most favorable circumstances for the claim of unusually high numbers of hate crimes against white people based on their race: I'm going to assume that every murder that was committed falls into that category (I hope I don't need to point out how exceedingly ridiculous this notion is).
According to the statistic linked above, there were 17805 murders in 2014/2015 in South Africa. I use this period because according to wikipedia, there where 4,554,800 white people living in South Africa in 2014. If every single one of those murder victims had been a white person, this would mean that 0.391% of the white population would have been murdered that year. That would mean that out of a group of 1000 white people, a little less then 4 would have been murdered. Additionally, for the claim to be true, those not-quite 4 people would have needed to be murdered because they were white.
To contrast this with other causes of deaths, I looked at the official statistic for 2014, and this is what I found:
Causes of death with similar percentages are mental and behavioral disorders (0.4) and diseases of the musculoskeletal system (0.4). The only causes of death listed with an even lower percentage are skin disease (0.2), pregnancy and childbirth (0.2), and diseases of the eye or ear (0.0, respectively). Now unless we assume that an "organized violent campaign targeting whites" (question title) was less deadly than non-transmittable diseases that are usually considered non-lethal, and in fact only a little more deadly than skin diseases, I do not see any way to make that claim even remotely plausible enough to seriously entertain.
It does not seem that even far-right outlets claim a genocide according to a widespread definition of the term. If the claim is about an unusually high level of hate crimes against white people based on their race, there does not seem to be any evidence commensurate with the claim.