So, first you say something false, but do not acknowledge that, and then you quote something, without attribution, that has little to do with per capita crime rates, which have been higher in republican-led states for decades.
By the way, there are many factors for migration to cities in republican-led states, but arguably the most influential is economic: those cities are, relative to cities in democrat-led states, less expensive to live in. And they are that way primarily because no one until recently wanted to live in them because they are, by-and-large, poorly managed, with poor investment in infrastructure, social services, and amenities. And most of those republican-led states (and their cities) are heavily subsidised by the democrat-led states (and their cities)—if the federal redistribution funding was cut off to all states right now, most democrat-led states would have budget surpluses, whilst most republican-led states would have massive budget shortfalls. A few would immediately go in to bankruptcy, such as their dire financial state without government subsidies that mostly come from democrat-led states.
Ultimately, the cost of living crisis—and the American dream of owning a home—drove largely progressive, middle class people to migrate out to lower cost of living areas. Not only did they not bring the crime, they actually brought tax revenue and demand for better infrastructure, social services, amenities, and political change (which, in turn, has lead to policy change). Many of those cities (and even some of the states) have seen moderating trends toward progressive values because of the mass economic migration. They are not voting with their feet for republican policies—they are moving where they can afford to live (i.e. places where there was relatively little demand for housing previously) and then working to change the political environments where they have moved.
The irony is the trend you have incorrectly cited to try to erroneously explain the phenomenon of republican-led states historically having higher per capita crime rates than democrat-led states, that refutes your original claim that you have not acknowledged is false, is itself an example of mostly democrat/progressive migrants improving conditions in republican-led states.
Again, I am a trained economist, so I am happy to go well in to weeds on this.