Sure, Conway's Game of Life is a toy problem, but the optimizations used to make it run fast (which go way beyond mere bit-twiddling, btw) are useful tools and practice in a programmer's mental toolbox, for solving real problems.
Certainly, a programmer who "merely" plugs frontends into backends with databases or whatever it is that you consider a "real job" in programming[0], doesn't need to know about bit-level optimizations to do that job. But I would argue that even then, it makes a better programmer, knowing about that sort of thing, broadening your bases, versatility and well-roundedness.
Doesn't mean you have to use it on problems where it's not supposed to, or premature optimization.
Elsewhere in this thread you say you don't need low-level optimizations because Redis handles this for you. But you wouldn't say that the people researching, designing and building Redis weren't doing "real jobs", would you?
I think broadening your bases is actually a pretty good reason for learning about these (or other) things. Because you seem to have a pretty narrow view of what a "real job" is in programming. In particular that you can't seem to come up with any good reasons for knowing about bits, except IEEE floats.
What about graphics programming, usually pixels are packed into a 32-bit RGBA word, you need some basic bit operations for this. Most situations abstracting that away kills performance.
If you need to read out sensors from a device, you're probably going to come across bits (and many other ancient programming lore) somewhere along the line.
If you write code for small / low powered hardware (like Arduinos or equivalent) you are going to need to know your way around bits and bit-manipulation code is very welcome there.
Knowing about these techniques is also important because sometimes they suddenly become useful in a whole new or modern context. Take antirez's Feistel network approach to this fizzling-problem, for instance. That's a cryptographic primitive now used in a graphics context. You can make exactly the same point about it, that a programmer who is supposed to do frontend/backend/db work, should never write code like that, and indeed this is true, you most definitely should NOT be coding your own versions of crypto primitives in a context like that (I'd argue that's even worse than bit-twiddling).
[0] I'm kidding, I respect the work that goes into it. I think it's boring as hell, but it's a lot of work and not all trivial either.
> (which go way beyond mere bit-twiddling, btw)
I was fascinated by optimizations people come up for Game of Life by reading Michael Abrash's Black Book.
> a programmer who "merely" plugs frontends into backends with databases"
I am such a programmer: never have used bit manipulation in my job, and while it is kinda boring, it is a job, and someone has to do it.