Ultimately the answer will lay in whether you want to get married, or not, and whether OSM can source open-GPX, shape files, whatever, for all the UK Ecclesiastical Parishes.

Until the Parish Councils Act of 1894, there was zero difference between a Civil Parish and an Ecclesiastical Parish. The 1894 act extracted all non-Church features & vested them in newly-created Civil Parishes. The principal feature that the Established Church retains, and which affects all members of the public living within an Ecclesiastical Parish, is the right to be married within their local Church. Now obviously, in order to be able to know which is that ‘local Church’, a person needs to be able to search for it upon a suitably equipped map. At this moment, that is NOT OSM.

example: the Porchester Ecclesiastical Boundary

11 September: I stated in my 27 August Diary that “The Ecclesiastical Boundary runs down Marshall Hill Drive”; not true. The vicar at St James, Porchester, the Revd. Phil Williams, gave me a copy of the Porchester parish boundary (many thanks to him) and the Boundary runs along Valley Road and across the bottom of Marshall Hill Drive, and then up Simkin Avenue. However, at no point does it run up (nor down) Marshall Hill Drive apart from that tiny little segment at the bottom.

For reference, the Porchester Ecclesiastical Boundary (Diocese of Southwell & Nottingham, Gedling Deanery) that the vicar gave me was traced on an Ordnance Survey map (grinds teeth) and only part-follows existing streets:

Starting in the north-west corner:

1. Mapperley Plains (B864) junction with Spring Lane
2. Spring Lane junction with (uncertain, though probably Gedling Country Park)
   On the OS map this appears to be a mysterious ‘103m’ marker to the east of Crimea Farm, but neither of these waypoints are on the OSM map; indeed (mental note), the whole of Spring Lane needs a thorough survey. The boundary falls south through the wastelands of the former Gedling Colliery, passing by the Household Waste Recycling Depot (closed).
3. Arnold Lane junction with (uncertain, probably High Hazles Close)
   High Hazles Close is on the other side of the road, and the actual junction is to the east of that road. A stream is reported to be culverted and to cross Arnold Lane at that point, so that is a likely way-marker for the ancient boundary.
4. West up Arnold Lane to junction with (most uncertain)
   It is clear that the Ecclesiastical boundary was established before any of the current streets in Phoenix Farm estate were created. At some point before the old service road for the former Recycling Depot it leaves Arnold Lane and falls SSW, missing High Hazles Close but slicing indiscriminately through The Fairway, Sherwood Academy and Chesterfield Avenue before hitting near the end of Rufford Avenue, travelling west along that road just beyond Welbeck Avenue, then travelling at a strange angle south west towards…
5. Westdale Lane East junction with (most uncertain)
   The boundary has finally hit a patch that I’ve surveyed! In fact, the boundary joins Westdale Lane at a point north of Westdale Court (service road) (probably opposite 217a) and, as it happens, I updated the map there yesterday. I recall nothing to suggest a way-marker.
6. West along Westdale Lane East to junction with (most uncertain)
   The boundary doesn’t quite reach the end of Westdale Lane East when it turns south-west, passing through Mapperley Furnishers and running along the top part of what I called at the time wet dead-rat walk (because it was raining & there was a dead rat on the tarmac). However, whilst dead-rat walk turns left the boundary carries straight on, running along the bottom of all the gardens between the bungalows on Elmhurst Avenue and the semi-detached houses on Portland Road, then does the same for Fraser Square until, after crossing Gardenia Grove (which runs along the brow of Marshall Hill) it turns from SW to SSW and finally joins the existing road network near the top of Ernest Road.
7. Ernest Road junction with Valley Road
8. Valley Road junction with Marshall Hill Drive
9. Marshall Hill Drive junction with Simkin Avenue
10. Simkin Avenue junction with Donkey Step walk
11. Donkey Step walk junction with Hillview Road
12. Hillview Road junction with Florence Road
13. Florence Road junction with Porchester Road
14. Porchester Road junction with Moore Road
15. Moore Road junction with Whittingham Road
16. Whittingham Road junction with Woodborough Road (B864)
17. (north back to the 1st junction)