The fighting was because civilization was falling apart. Without the hope of new generations things crumbled.
Crumble != all-out war.
Humans have an energy budget, and they do not spend meaninglessly. The people fighting were expending a ton of energy, so they must have had a cause. But what cause is worth engaging in major combat operations over when there is no future?
The people in that world would have reevaluated the cause to fight given their new surroundings. But that's not what the movie showed -- it showed stereotypical war scenes; i.e., scenes of people fighting for a future.
When facing extinction, self-image is devalued. Things would become more basic. Fights would be instinctual -- vicious, but short. People could manage to band together to take care of a problem for a time, but that could not be maintained for long as they would want to break up to return to their solitary depression. They would not stand having their energy budget be under the control of someone else for very long -- they would want it for themselves, to seek after what small personal desires they had left. The large "causes" would just no longer be meaningful when everybody's going to die.
The baby was in danger because there were those who were interested in not seeing the baby born.
WHY?
If they had slipped into, "Everything is meaningless," the baby would be meaningless -- they wouldn't care one way or the other. But if they had meaning to their lives, then the future would have meaning, too, and you need babies to have a future!
There's no system common enough for a group to form that would desire to kill the baby. An individual can have an aberrant value system, but an organization isn't gonna pop up to service it.
They never showed a value system that valued X and that a baby was in contradiction to. So why would anyone be against a baby?
If they had set up that this was a new whack-job religion, that would've at least been something. Kinda cliched that religious people are mindless fools with no sense or morals, but at least it fits reality.
The "meaningfulness" of the baby in the big picture was sort of the whole point of the movie. The journey of the movie was Clive Owens' character (who is in every shot) arc, as he starts to find purpose in life, both micro and macro.
What one man thinks is irrelevant, especially as his journey wasn't shared.
Nothing external ever changed.