People who think it's high taxes which cause people to flee high cost state, they are ideologically blinded, naive fools. High taxes are a part of the reason but it's rent which really impacts people. Only rich people have the luxury to worry about tax rates.
Rent is partially fueled by property taxes.
It's a neglible impact. With high taxes, some investors are less likely to want to buy rental properties so fewer are built, which can drive prices up slightly. However, there's no cabal of landlords arbitrarily setting prices as a direct function of tax rates. Prices are a function of how many units there are versus how many people want to live in a given area. Landlords can either charge the going rate for the properties they have or the units will sit vacant. Like many underpoulated cities, we have very high property taxes here in Memphis along with some of the cheapest rents in the nation.