Here's an unbiased source.
https://worldpopulationreview.com/state-rankings/population-decline-by-state
People are indeed getting the hell out of certain blue states, NY, CA, and IL, probably cause they're fucking expensive to live in - at least in the big cities where most of the population is.
And FL, TX, ID, SD, and MT are picking up population. ID, ST, and MT are tiny population wise so any change there is a blip, but people seem to really be moving into FL, SC, and TX, for whatever reason.
This data is a couple years old so it wouldn't reflect recent legal and political changes.
Here's the thing though. Changes in total population of a state on this list are all between -1% and +2%. That matters, but it's not like whole towns are being depopulated or anything.
The brain drain issue -- doctors fleeing red states -- sounds like it's considerably more dramatic than that, given that most TX counties have zero gynecologists and a significant fraction have zero doctors.
Bold of you to assume he started with actual data