Life expectancy increases tend to decrease birth rate. And with Elon Musk currently working on colonizing Mars, and seasteading making some progress, there will likely be a lot of place to live in by the time we work out aging. Actually, if both fail, there is a place for 6 billion more people on Earth.
You're afraid of your own prejudices about something that isn't even here yet. And I don't understand your use of word "immortality": it is aging we are discussing here, a condition that causes people to die, often in misery and pain over long periods of time. I think it is a very humane, global, noble cause, and I honestly don't understand how you can be so cynical about it.