What traditions fully embrace the concept of a "local parish church"? As far as I understand it, the concept of having parishes and parish churches means that regions are divided up geographically, that each region will have a church that is specifically dedicated to that region, and that everybody in that region is expected/required to be a part of that local church.

I know that there is a huge variety when it comes to implementation. What I would like to know is what modern traditions fully embrace this concept to the point of enforcing it on some level. Are there any traditions that would refuse to let members cross parish lines to attend another church? Do any others with perhaps a less hard line rule have specific doctrines encouraging this but define exceptions where it might not be required?
The Church of England falls into the &quot;partial&quot; category. There is a parish system of around 13000 parishes in England [that's not Wales or Scotland, which have their own autonomous Churches] each with at least one parish church.
Residents in the parish can be baptised in their parish church; baptised people can be married in their parish church; people who die can have a funeral either in the church of the parish where they die or where they lived.
There are some exceptions which extend these permissions. Residents can be baptised in another church with their parish priest's permission. There are &quot;qualifying connections&quot; which can be made with other churches to allow marriage — for example where your parents have worshipped. And there is nothing stopping you from attending church outside your parish and joining the electoral roll of the church you attend. That effectively makes you a parishioner.
Because the Church of England is a broad church with a variety of liturgical practice [and associated theological belief] it's not uncommon for people to &quot;shop around&quot; to find a church which suits them.
The church where I was churchwarden* had a particular ministry to its little bit of the country, an urban situation with a high population of poor and homeless people.
Shameless plug: Go to this map on A Church Near You and enter your location. The parish of the place you select is highlighted, together with local churches. I'm responsible for some of the coding behind that. If you're very lucky you may even find a parish with more than one non-contiguous area, or a tract of land which is not in any parish at all. Anyone resident in such an extra-parochial place can attach themselves to an adjacent parish. The map is intended to provide a service for potential churchgoers to find their local church, or for engaged couples to find their parish church (in order to simplify the process of a church wedding).

*Churchwarden: an ancient layman's elected office in the Church of England with particular legal responsibilities for finance, buildings, ministry and parochial management.