An average of 2 surviving and later breeding children is necessary to sustain a culture. That may work out at 2.3 overall for all I know, it'd depend on its health service and percentage of surviving offspring.
But a culture whose people have realised they have expanded too much, and that it is irresponsible to continue expanding, may well instinctively do the right thing overall (irresponsible individuals bucking the trend) and contract a little.
For sure this does not prevent being swamped by less enlightened cultures who do not have the same advantages, and could be a concern; but that seems the lesser problem at present. We can not sensibly continue in a "who can grow the biggest" race between cultures. But if the society in question is sensible it will restrict immigration spoiling it's good efforts.
Meanwhile one can only hope areas of the world that do overbreed reach a stage where they too realise and do something about the problem.
What I don't understand is why the question is put in a religious context. A society can have many religions and yet I believe there is a tendency to move towards the country's typical family size rather than stay as an isolated group adhering to some religious 'norm', is there not ? immigrants may be less willing to adopt the local behaviour, but second and third generation ?