We may be on par with them in terms of nominal rates, but those other states' property taxes rise with the value of the houses every year, whereas CA prop tax amounts are based on the cost at the time of purchase and adjusted at a max of 2%/year, even if their house appreciates by 10%, as it does some years. People who bought their houses in 1975 are paying taxes based on what their houses were worth in 1975 times roughly 1.02^40, or 2.2x. In the same period, the median home price went from $41,600 to $478,700, a rise of almost 12x. So, if they moved to an equivalently valuable home, they'd pay about 5.5x the amount of tax going forward, which can be very significant.

Housing prices take into account the amount of taxes one expects to have to pay, so if they're no longer locked, and one expects prices to rise, then the price one will be willing to pay will be lower. Also, prices will fall as more supply opens up, since there won't be such a big advantage to sitting on houses anymore, and people are more free to move to less expensive areas. Currently there's a bit of a rent control situation where the low rates can be passed on to your descendants, and there's a big incentive to stay in it rather than selling it and moving farther out, even if the place farther out is half the price. This effect is more pronounced on the high demand areas where prices have risen more.

Over time, the prices would adjust and settle. People may end up paying more tax overall, but we can play with the rate, or we could decide that the schools could use more funding (in many places, they could), and that we should keep the rate where it is. As it is now, the people who are just moving to CA are heavily subsidizing people who have lived here for a long time, and the lack of liquid housing supply is causing prices to shoot up.