What then would be the branch of literature which deals with the reaction of human beings to life in general, and uses changes in science and technology as a backdrop and overarching metaphor for those reactions?
I think the main divide between SF and fantasy in most people's mind's is that in SF technology most regard as "futuristic," regardless of how plausible it really is, contributes significantly to the plot or setting.
If there are space ships, it's SF, even if the drive isn't well explained. The point is that humans got off the dirtball called Earth and interesting conflicts ensue as our our society evolves in interesting ways as a consequence of that.
People can certainly still struggle with issues that are relatable to modern readers and which come up in other genres too (like love and hate and all that). To some extent, they have to. If the situation (or characters) is too alien, it might be hard for readers to do this.
Hard versus soft comes down to how central the tech is to the story in some cases, and how well explained it is.
Dune is usually billed as hard SF, bit really it isn't. It's more about the power struggle itself, and the personalities involved, than in explaining why or how spice allows people to morph into navigators that can warp space with their minds. Really hand wavy, fantasy really. And the desert planet with a breathable atmosphere and tolerable day and night temperature fluctuations is a "kewl" setting that makes no sense ecologically or with reference to the laws of physics.
But it's really not important if it has internally consistent rules and people love the story. In this case, it's considered SF and not fantasy because it takes place in the distant future, on a planet that's somewhere in our "real" universe and humans got there in a space ship. The powers that people have in that universe are not supposed to be magic, but instead are bestowed by something concrete and physical--spice--even if it's handwavium.
Not everyone's cup of tea, of course.
The line between SF and fantasy do blur sometimes, even a lot. I think it's inevitable. The more we try to nail something down sometimes, the harder it can be.
Really, we like what we like in speculative fiction. And sometimes the exceptions to our own rules are the most baffling of all.
Another example is a book by Jack Chalker. He had a planet that, since the axial tilt was so steep that it was like the planet was laying on its side, the planet had no seasons. Unfortunately, that scenario guarantees extreme seasons.
Yeah, that sort of thing annoys the crap out of me, because it suggests that the writer not only didn't do his or her homework, but simply didn't think things through. I get that a lot of these stories were written back before the internet made for easy research, but it's not that hard to logic that one through. Want a world with no seasons? Just have a world with no axial tilt. Fifth grade science (at least it was back in the old days--I don't think they have science in most grade schools anymore). Done.
A minor pet peeve of mine is the huge number of writers, SF, fantasy, and even contemporary fiction, who have no concept of the relationship to the moon phases and when the thing will rise and set.