I'm still not allowed to comment in order to clarify some stuff, so I will just assume stuff as I write here.
Far into the future
I'm gonna start by saying that true immortality in the sense you mean (against aging, decease and even murder - true immortality) can only be achieved hundreds, maybe thousands of years from now.
In such a future, humans have already mastered biology and genetics to an extent that they no longer need to worry about death, it's only logic to assume that other areas of knowledge - history, geology, philosophy, sociology - have evolved as well. That being said, a future society should be kind of utopic in a sense that humans probably reached a level of societal understanding that ended (or at least mitigated, to a peaceful extent) conflicts about race, religion, politics and stuff like that. There might still be differences, but the general society knows that conflict is not the way to resolve them.
They're a society that has learned to look back and not repeat the same mistakes. There is no murder because they do not murder. There is no decease 'cause they erradicated most deceases. And they live forever 'cause - as I stated before - they mastered aging to an extent that everyone is healthy and young forever. And if a deadly accident happens... well, I'm sure you can figure out a good Altered-Carbon-like explanation to justify those people not dying.
We got to the point where society can only grow.
If we consider that our planet is overpopulated already (and that's really not bound to change in the near future), I'm saying that the next step is reducing the population to a sustainable amount. I'm assuming that even though humans transcend death, they still need to eat and consume stuff. Since the earth has finite resources, there's a maximum amount of humans that the planet supports.
The ethical answer to the constant's problem would be the colonization of enough planets to sustain the given amount. The unethical one would be the random exilation of millions.
Regardless of the approach, once the constant is reached there's a single logical answer: sterilize everyone. This should do it.
But now you have another question to answer: Won't more humans ever be needed?
By answering yes, you state that the population has to grow for some reason.
In Huxley's Brave New World, humans are created in labs. There are bases scattered all around the world where humans are produced via genetic manipulation to perform a deterministic function that will ultimately define their place in that world's society. Let's assume that the social standing problem shown in the book is not present here.
Assuming that some kind of government or organization capable of creating designer babies exist, these people would also have to be responsible for maintaining full control of two variables:
- The number of humans that exist today; and
- The number of humans needed.
This number of humans needed implies that humanity has a certain objective that demands more people in order to be achieved. From this point you have full narrative liberty to determine a feasible reason for the population to grow.