Yes, but no one is really complaining about "not enough kids." They are complaining about not enough kids of their preferred skin tone. So they see immigration as an exacerbation.
I can't help but agree here. "Declining birth rate in the western world" just comes across as a dog-whistle to me. I guess I kind of only alluded to this myself with my response that they were being "weirdly cagey", and I wish I had been more direct like you were willing to, so thank you for this