This is a common refrain in US conservative discord, but I'm somewhat skeptical if it's as influential as some believe. I personally think single motherhood and the general soy-ification of the last few decades of men is what is really driving these trends, and focusing on migration takes away from the bigger picture. As the service sector/FIRE economy has grown in America, so has the number of weak (woke) men. Here in the midwest, you see tons of kids of who grew up in super conservative small towns, and they come to the big cities for university and/or service sector work and of course become raging leftists. In the past, most of these kids wouldn't have had the luxury to move to a big city and spend their 20s in a state of extended teenager-dom and debauchery. The only thing keeping conservative states red is their rural populations, virtually every large urban center in the US is a blue lock. The suburbs are no longer a red stronghold as they once were either. Western states tend to have much sparser rural populations, which is why Portland heavily overshadows all of Oregon. I'd argue what we are really seeing is the increasing urban/rural white/blue collar culture war.
Colorado is likely a victim of the migration you speak of, because its arguably the premier outdoorsy state, and as been a huge destination for decades now. When people say this about a state like Texas though, I'm skeptical. Many Californians that move to conservative states are in fact conservatives already. Leftists are often incredibly ignorant and fearful of anywhere outside their utopias. It's certainly a factor, but I think replication of the ideology itself is still a far bigger threat than migration.