In this scenario we are assuming there are enough individuals to bring the population back to a stable level, but if any more die or refuse to participate the entire species is doomed to extinction.

The question, in my mind, comes down to this. Does one half of a population get to decide whether or not the whole species goes extinct?

I would argue that they don't.

On the great scale of morality, IMO, forced extinction is infinitely more heinous than rape. Rape is a horrific crime and often causes life long trauma, but it is still a finite period of suffering.

Extinction is permanent, the end, for all time.

Now, you could ask "well, why does one half get to decide for the whole species to not go extinct?"

And for this I truly do not have an answer or at least not a pleasant one other than my gut feeling is that if eminent and certain extinction can be avoided than fundamental human rights can be violated in its pursuit.