You are right to an extent.
First, if the inclination to have more or fewer children is at all hereditary, there is a strong natural selection effect over time. Evolution in action.
Second, (sub-) societies don't have maintain themselves via their _own_ children. Priests in the Catholic church were famously barred from having children for at least a few hundred years by now. Yet, the Catholic church persists. Similarly, throughout most of history cities had below replacement level fertility, just because we didn't have the hygiene and medicine necessary to keep the diseases at bay. Yet, cities persisted.
You can say that they have been 'replaced', but so are families every generation. Drawing a strict line is only possible, if you put an undue emphasis on genes only.
You are right however, that for a culture or 'ideology' to persist, you need to replenish the pool of people in some way, either with children or converts/immigrants. (Or, I guess, you can figure out immortality for your members?)
Almost by definition, migration/conversion can only be an option for the most appealing of societies: those migrants have to come from somewhere; they are other people's kids.