What you’re partially describing is the demographic transition model, which splits population growth into five stages. The first few involve birth rates remaining high as a country’s development decreases death rates leading to the birth rate decreasing to match the low death rate. The last stage appears to be a little more uncertain than the last time I read up on it, at that time the standard expectation was that birth rates fall below the death rate in highly developed countries leading to a population decrease.

The problem I have with your thinking on the matter is your focus on “brown people” and the use of immigration to keep population growth. Immigration is just a stopgap solution for population decline because it relies on the existence of other, less developed countries for people to immigrate from. But those less developed countries (I assume the brown people you’re talking about) are also stepping through the stages of the demographic transition model as they become more developed, meaning eventually when the whole world is developed the overall population will peak and then decline. At that point, immigration-reliant countries like the US will have the same problems as anti-immigrant countries are starting to run into now. So the problem itself of population decline is not artificial, different developed countries at the leading edge of the charts are just dealing with the natural trend in different (and sometimes racist) ways.

It is a crisis for capitalism, but as long as humanity relies on systems based on an increase of the fundamental economic unit (the consumer), it is a crisis for humanity as well and we should worry about how to alter those systems. Places like South Korea and Japan are the first to have to deal with that shift, but the rest of the world should be paying attention to what does and doesn’t work for them because we’re next.