During about the last 30 years, Texas has picked up hundreds of thousands of people fleeing California. But in that same time, Texas has gone from strongly Democrat to strongly Republican. See https://en.wikipedia.org/wiki/Politics_of_Texas for details. Of course wikipedia is very left-wing so the "analysis" is largely left-wing propaganda, but I don't think they just made up the statistics.
How can this be? Because most of the people fleeing weren't left-wing Democrats, but people who just want to be left alone.