I live with the back of my house to a Runway that runs north to south almost perfectly. I live on the west side of the runway, Across the street from me on the further west most side of the road lives my neighbor who owns runway rights,(his house is completely unconnected to the runway) which from my understanding grants him parking privileges at a designated area on the runway itself. does owning runway parking rights make it legal for him to taxi his plane all 200 yards down the residential road in between my house and his to park his plane in his yard?
It doesn't matter whether or not the road is residential, it depends more on public or private. If the road is a public road, taxiing an aircraft will usually not conform to state motor vehicle regulations without a pilot car and a permit. In rural areas where nobody cares, it doesn't matter. When there are enough people around somebody will object, and then it does matter.
An airpark preserves community access to a runway via residential roads by making them private, and not subject to state or local motor vehicle law. Rules are enforced by conditions on titles to property, or by reference on the title that the property is subject to rules made by an HOA or other organization of the sort. Look at your title.
I think it unlikely you bought into an airpark without knowing it, but if your street signs look like this, taxiing on the streets is probably legal.