The PAO wins, because its a "voluntary" association, whose regulations and by laws can be more strict than that of the governmental entity (State, County, City) in which it is organized, but not less, so long as they don't run afoul of certain "no no"s like restrictions on race or religion. To limited extent, they can even make use of age restrictions.
and typically, the States which are most "permissive" at the State level, such as TX and FL are "home rule" States, meaning the Structure of the State's Constitution devolves much of its general Police power to the local entities, the State retaining very little authority to over rule the zoning restrictions of its municipalities, or the HOAs/POAs formed within them.
The flip side, States like CA, tend to be MUCH less permissive at the State level, but keep greater control (and ability to set aside) the covenants on land use of entities formed under color of State law.
Don't like it? Move.
Or run for office in your HOA/POA and change the bylaws.