Will modern cosmology survive into the future?
We are only 450 years into the 'Scientific Revolution', and not barely 100 years beyond the dawn of modern atomic physics and relativity. Modern cosmology as astronomers practice it is less than 80 years old. Yet, despite the youthfulness of this scientific approach to the physical world, there are basic underpinnings to modern cosmology that have proven themselves to be spectacularly robust against new generations of data that have been gathered. I think that modern cosmology has already proven itself capable of creating theories that are capable of being tested rigouously and falsified. What will probably not change, however, is the general public's fascination with what they perceive as 'conspiracies' and 'narrow-mindedness' among mainstream astronomers. There will always be endless media polling of the 'underdog theories' which are believed by non-main stream astronomers.
Modern cosmology as practiced by astronomers will most certainly survive, although we can expect that some details will change as we learn more about the distant 'young' universe and dark matter. Our certainty in a particular cosmological theory in the 21st century, however, will probably always be construed by some people as a 'power play' by an astronomical mafia.
You might also consider that the fuzzier a theory or an explanation is, the greater its longevity because its language allows many interpretations. Science is not, however, about semantic word-splitting. Because it is based on only the best data we can muster, scientific explanations have a level of certainty and precision that virtually every cosmological idea prior to 1900 could never muster. Whether a scientific idea survives or not now depends on how well it compares with detailed observations. This makes every scientific theory exquisitely vulnerable.