Is there some reason to do this other than ideological protest?

For US citizens there is the global taxation rules. Is there something like that for UK citizens?

[delayed]

To the sibling comment: It's in case you wish to acquire citizenship in another country that does not recognise dual citizenship.

I.e. that [new] country will not allow you to become a citizen of it unless you renounce your original one.

What that might actually mean practically, or if you can un-renounce it later, I don't know. [Edit]: Turns out, according to that page, yes, you can do that with some kind of bureaucratic shuffle. Daft - but sometimes these things are.

You've had another reply which describes the process to renounce your British citizenship, I'm wondering if you just weren't aware of that, or is there something else backing up your assertion?

South African citizenship can be renounced. https://dirco.gov.za/berne/renunciation-of-south-african-cit...

As for why someone might do it, some do it to ensure they're not at any risk of extra-territorial application of South African laws, especially tax laws.