It is quite dramatic, but I suppose the foreign office has to highlight any possibility of crime. I have not looked at other countries warnings, so as a South African:
Surely many of these points are not just affecting SA. Are most places not at threat of some terrorism with everything going on right now? Not that we have had any warnings but obviously this affects everyone at the moment.
Like going to any city as a tourist, you have to be sensible. Do not think you would like to go and get a good view of a township late at night in a fancy hire car, as you are going to stick out like a sore thumb and be a target. By all means, do these things, but go with a guided tour.
Don't walk around flashing off designer items, not that people don't have these things here, but majority do not, so that in itself will make you a target.
Pickpockets are everywhere. Like most cities. Do not walk with your iPhone in your back pocket or leave it laying on a table while you eat.
There are protests from time to time. But it is very unlikely these will be in a tourist area. They will be in industrial areas most likely, where workers may be striking for higher pay, although there were some extraordinary one a few years back related to Jacob Zuma release.
To travel, only use Uber or Bolt. Do not use local minibus taxis as a tourist. Cape Town has a great bus system called MyCiti. You can get a weekly pass and you can get to most places safely. Again, just be vigilant.
Loadshedding - power cuts. Yes they are a thing. The power will most likely go out according to the schedule at certain times depending on the stage of loadshedding. At the moment we have none so we have full power. It can go up to stage 6 when the power will be out for 6 hours or more. Most accommodations/restaurants/all shopping centres have alternative power sources. Generators, solar etc. You will need to enquire about this when you book places. If the power is out and you have hired a car, the traffic lights will be out and you will need to then treat those as the four way stop.
If you hire a car and go to shopping centres etc, places with a fairly big car park which is free, there will no doubt be car guards. They watch your car. Basically they are foreigners into SA and this is their income. Tip as you feel at the time. Do not feel obliged to tip every time though as if you are making lots of quick stops then it adds up.
With that out the way, I can also say that I think you may find it hard to find a more friendly nation. You will eat good food and drink great wine. You will more than likely have decent weather. You will be made to feel welcome. The ocean is pretty damn cold on the Cape coast so you will be quite refreshed after. Or you can take a boat cruise. If you choose to you can see wildlife galore, including whales. If you are not veggie, have a braai and try some biltong and dried wors.
But you will see poverty, and you will see the huge divide between the very wealthy and the very poor. You will see children begging on the street. This is the reality of being in a 2nd world country.
I have answered as honestly as I can so I hope this has helped with any thoughts/doubts you may have been having.