Whereas I think that civilization is more resilient than most people think - in fiction there’s some event and a few years later the whole planet’s a desert. In reality I think that people will carry on - perhaps despondently, but they’d carry on.
And actually as extinction-level disasters go this one is really gentle, at least for the first few decades. Existing society will be essentially unaffected (unless you’re Dr. BabyCatcher), with existing families with all their children and babies carrying on unaffected. Some people will freak out over the fact they can’t have babies, but a good percentage of the population already can’t or don’t want to have more children. Some people will freak out over the impending existential end of humanity, but that’s a pretty high level concern, and people still need to (and can) go to work and draw a paycheck. While some people will be troubled by the impending end, we’re talking about something that’s half a century away and most people can’t internalize problems happening a month out.
The religions would be wigging out because they’d be trying to fit this into their predictions about the end of days, but everyone else both has to, and has no reason not to carry on as normal. Except Dr. Babydoctor, and Kelly Kindergardenteacher, and one career after another as society slowly, slowly spends the next century gently fading out. (Until power and food distribution finally fail, but that will only be in the final stages, and everyone will see it coming a mile off and maybe do something about that too.)
And no, I don’t think that sperm preservation is a viable way to preserve humanity. Certainly not all of humanity, and while you might have pockets of such people, enclaves of baby-manufacturing civilization, I have doubts that any such enclaves would be large enough to form viable populations. Particularly once their sterile neighbors find out about them.