The answer is something between marketing and more incentives for families to have children (usually tax based).
But if you look at it from the perspective of there not being indefinite amounts of oil left, less population growth suddenly looks more like a solution.
The issues as always are the transitioning phases.
So for example, if the baby boomer generation can dominate politics, simply by mass - this becomes an issue.
If we dont have the same growth built in into our economies - this becomes an issue.
If the only supposedly positive concepts and outlooks, that are floating around, are based around "saving the world" and "reducing climate change", that has limited growth potential - and no immediate local impact, so - this becomes an issue.
The thing is though, that going back to old solutions (that hardly worked back then) isnt the solution either, because the world develops around us (thats the globalization argument)...
So this becomes a complex issue.
If for you its just "prolonging your cultural heritage" its not, but if you look past that - it becomes a more complex issue, very fast. And in terms of prolonging cultural heritage - you would be amazed, how much cultures tend to change even in conservative countries over the years. Go back two generations, and you wouldnt recognize your own country - regardless of how progressive it was.
So after a while the "do I feel at home" argument lingers more around language than anything else. And if you look at that with an "agist" filter as well - the anti-immigration sentiments are caused by the same people who caused the population decline in the first place. And they did it to top off their economic status - from a base level, that their children never will reach.
If they'd now tell their children, to regress on womens rights to "solve this" because they want to feel more at home in their old days, that wont go over well. Apart from, that that wouldnt help.
Direct correlation from feminism to lower birth rates is questionable as well. They just were around at the same time.
Look at your parents. They caused the problem. Were they really that feminist?
I'm inclined to call rightwing BS.
Count years, and get to the same conclusion.