Oh, Merriam-Webster has it somewhat different, a parishioner is “a member or inhabitant of a parish” and a parish is specifically for “a local church community composed of the members or constituents of a Protestant church”
I don’t doubt yours is probably a much more original definition, and theirs is simply reflecting more Left Wing influence.
IMNSHO, the M-W definition reflects total ignorance of the Reformation and certainly didn’t get input from a Southern Baptist preacher.