Heck, that effect was the entire reason for Bloody Kansas, with pro- and anti-slavery people moving into the territory in order to influence its politics. It's why the Free State Project exists. It's why some politicians want to decrease immigration, and others want to increase it.
I'm curious why you think it doesn't exist. It's hardly an extraordinary claim, and makes perfect sense: people from a place have the habits of mind common to that place; when they move elsewhere, they retain those habits of mind for some time. Even if they were outliers at home, they are more likely to be like their former neighbours than a random subset of their new ones (ever noticed how much you have in common with a fellow countryman you meet whilst travelling abroad? It's the same effect).
And when there is a tremendous influx of people from one particular place into another particular place, then one will be more likely to find people from the former place in the latter — that's just math.
Maybe you find this good, but I don't: we should try to figure out what makes a state the sort of place people move from rather than the sort of place people move to, and replicate that.
(in California's case, I think it's the sort of place people move to because they must and from because they can)