I could be completely wrong, tax stuff confuse the hell out of me...
That's pretty much the definition of regressive when it comes to taxes - people making more are being taxed less, proportionally.
Formerly 15% + 0% (if you lived in WA) capital gains one year is now 20% + 3.8% + 14.3% (if you moved to California in 2013). That's a pretty big difference for the same gain.
Of 43 states with individual income taxes, 7 have flat individual income taxes. [1]
That certainly seems like an argument that could be made, but I don't see that ownership of real property alone is a better proxy for "standard of living" than income is, so I don't see how any such argument would be relevant to the claim made with regard to property taxes. (Consumption -- as is the focus of sales and use taxes -- is probably a better proxy for "standard of living" than real estate ownership is and might be better than income, but I still don't think flat consumption taxes are more progressive against standard of living than progressive income taxes are.)
Your governor believes many (if not most) Federal assistance programs are unconstitutional. He believes in drug testing for the unemployed.
However: property taxes are significantly higher here (about $2-3 per $100 value, depending on location.) And you'll pay full sales tax on vehicle purchases (NC has a 3% highway-use tax only).