I took a while to ponder this point, to respond without writing a novel. To keep it brief, I’d say that whether it’s a regressive tax depends on the structure or the tax rates. Here in the U.S., poor people most definitely do not own houses, or at least not houses in high-value locations on lot sizes anywhere near the lot sizes that rich people own. Only people with money own big lots in high-value locations, like desirable city centers.

Our property tax system already contains terrible perverse incentives, such as taxing the value of land and buildings, which means that rich people can afford taxes on an expensive house, and middle-class people get slammed with taxes on additions and improvements to their houses.

Poor people rent, and landlords have the same perverse inventive to avoid fixing up their properties. Their taxes are lower if they let their buildings decay, keeping them just above the condition the building code requires.