well, that is the thing. If they could draw a random sample, it wouldn't matter if the population has changed because all that would show up in any truly random sample. But they can't get a random sample in the US anymore (they could come pretty close in the post WWII period using landlines and fixed geography area codes), but that's completely gone now.....) so they have to use a model, and the model has to be constructed from the past, so if the population changes, the model can't possibly be adjusted for it with any certainty until after the next election - at least other than by pure guess work.
What the pollsters are doing that is dishonest, is to continue to claim their polls have the same validity/accuracy level when they no longer do. Some of them will make the right guesses on their model and get the result, and then claim they are good pollsters, but in most cases that will be a fallacy. They simply made luckier assumptions about how to massage their model - i.e they have a certain expertise, but not necessarily as survey takers.