I disagree. The Rhodesians wanted independence, and they declared it. Just like we did. (Well, not quite). I wouldn't expect or want the Brits to come bail us out if we were attacked because of some ancient familial ties.
The Brits have no more responsiblility to them than we do. It's just as much our fault they're in the mess they're in.
I believe, though I am not an expert on Rhodesian history, and could be wrong, that the Brits did far more to the US to sell out the Rhodesians than did the US. If that is so, then I would submit the Brits do have more responsibility.
I understand your point, but would beg to differ. Were the Rhodesians descended from American settlers to the region, I would feel an obligation to fight for them.
At a bare minimum, I propose the Brits allow unlimited immigration from British descended citizens of Zimbabwe back to the motherland. My guess is that the Brits would be too cowardly and constipated and PC to even do that- not that America in this day and age is any better...probably worse, if anything.