Elsewhere (and better): 1, 2.
If one could go back in time and make a small difference in the past, would one expect it to effect dramatic changes to the future? Questions like these are fertile soil for fiction writers (generally writing under speculative or alternative history) but receive less attention in the historical academy, which tends to focus on explaining what in fact happened, rather than what could have been. Yet general questions of historical fragility (e.g. Are events in human history ‘generally’ fragile? In what areas is history particularly fragile? Are things getting more or less fragile over time?) are of particular interest to those interested in altering the course the long-run future by differences they make today.
The small but reasonably sophisticated historiographic literature in this area (e.g.) often uses analogies to chaos theory: whether minor perturbations in antecedent conditions can flow through into huge consequences, akin to the archetypal ‘butterfly flapping its wings causing a hurricane’ example. In defence of history being chaotic one can point to various events which seemed to have large consequences yet great uncertainty ex ante. Had Hitler been killed in the first world war, or was assassinated in 1944, it appears the subsequent course of the 20th century would have been very different. Although ‘great man’ views of history find little favour, many events seem to be contingent on the traits and foibles of particular individuals: whether the Nazi party would have risen to power, whether they would have prompted a world war, and the precise conduct of any such war seem to vary a lot depending on whether Hitler was alive and in charge.
The chaos of coital counterparts
I suggest chaotic views of history can draw considerable support from the sensitivity to initial conditions and large variation that attends any human conception. Conception involves one female gamete (which is replaced with a genetically distinct one on a monthly basis or so), and one male gamete from a pool of 100 million genetically distinct sperm (themselves taken from an even larger pool with roiling substitution). All manner of trivial contingencies scramble which two would fuse to conceive a child: if the parents decide to have sex another month, another day (or another minute), when they last had sex, ambient temperature, and so on and so forth. Siblings give us an impression of the variability of (forgive me) coital counterparts, and they are far from identical.
Moreover (somewhat like chaos theory) replacing one person with their coital-counterpart seems to cascade onwards to even more scrambling: not only do all the coital-counterparts descendants differ, but there is horizontal contagion if the counterpart’s slightly different behaviour influences others around them to only minutely change the manner of them conceiving children. Maybe there would have been something like the Mongol empire without Genghis Khan, but the precise details seem likely to vary. Yet these precise details may be decisive into which pairings between potential parents occur, and especially for exactly when they conceive, and the ripples of this activity goes on to perturb further successors, and so on and so forth. It seems not too wild to suggest that none of us would be here if the parents of Genghis Khan decided to postpone having sex one night until the following morning.
Constraints on chaos
Yet if whether an individual or a potential sibling exists is very fragile, many other parts of history seem fragile. Imagining the course of the 20th century where every individual is replaced with their sibling drawn from the genetic lottery seems nigh-impossible. Yet perhaps some very broad predictions (perhaps some technological developments, population growth, etc.) could still be confidently held.
One may speculate there is an issue of scale. Although maybe even very large historical events (e.g. a given empire, a world war) are seen as fragile, one could zoom out even further. If one was asked to summarise all of human history in a sentence, one may be able to include little more than, “Humans arose 300 000 years ago, and spent 290 000 years or so as hunter-gatherers. They developed agriculture 10000 years ago, and the industrial revolution happened about a hundred years ago.” These details seem pretty robust. There are broader contours of the human condition that constrain the course the eddies of possible people may take.
One may hypothesis more to the story than ‘stable over long run, very fragile over short run’. There seem some ‘meso-level’ factors which alter the balance of contingency versus necessity, and so constrain the fan of possibilities on particular matters. The technological completion conjecture might be one of these: although whether, which, and when great scientists are born may alter the precise timing of discoveries, they do get discovered not too much sooner or later: if Einstein was never born, the theory of relativity would have eventually been discovered.
By contrast, creative work does not have this property: if Dostoyevsky wasn’t born, The Brothers Karamazov would not have been written by someone else. Where ideas fall may vary between these: perhaps (e.g.) liberalism, democracy, and communism would have been proposed by an entirely different set of thinkers; the character of major world religions seems likely to be substantially different in worlds without (e.g.) Jesus, Mohammad, Confucius, or Buddha. To what degree these things vary is unclear, but perhaps not wholly intractable with careful study.
The goldilocks zone of future fragility
The value of efforts to shape the long-run future rely upon fragility being not too extreme either way. With very rigid laws governing history, the future is set regardless of what choices we make, and so directed efforts to change the future are as feckless as (on a Marxist view) a directed effort to prevent the eventual triumph of the proletariat. By contrast, ultra-fragile histories imply forecasting the effects of our actions on the future are effectively impossible, and concerted effort to achieve one end or another futile.
Intermediate views are not implausible: the future seems neither cast in stone nor flotsam borne by the vicissitudes of chance. Yet degrees and variations are productive to investigate: perhaps political history is too chaotic to steer, but technological development less so (or vice versa). I think these topics could reward further investigation.
 I leave other sources of ‘coital perturbation’ as a less-than-pleasantly-edifying exercise to the reader.
 A more proximal example is that whether a given person’s sibling counterpart is male or female is about a coin-flip. Given now and in the past there were incentives to have a child of a particular sex (consider the importance of having a male heir in many cultures), it is plausible (e.g.) a family’s male third child may never have been born if one of the first two was male instead of female.