And in many families in rural NSW there was very little 'stigma' during the early Victorian era as there were few clergy and long distances between small settlements. So what may have been 'stigma' in the English counties, may not have been so significant, beyond the seas, in the English colonies. At no stage in NSW colonial times was there ever a law/regulation/general order making the Church of England the Established Church. There was no Establish Church in NSW.
As NSW included a huge geographic area (from at least 1788 to say 1859 when Qld was hived off) it can actually be helpful to check the online indexes for NSW BDM to find BDM events recorded there for ceremonies held throughout the South Sea Islands, New Zealand, Victoria, Tasmania, Queensland, as well as what is now the much smaller land mass of NSW.
There are of course BDM for NSW events (NSW being that larger territory noted above) held by the (C of E) Bishop of Calcutta, yes, the sub-continent
for several decades commencing from the first settlement and for much of the penal era (so from 1788 forward into the 1800s) .
Even in the 21st century the tyranny of distance between localities throughout the continent of Australia has significant impact on the time it takes for a person to get to their local doctor, dentist, hospital (measure this in several hours in the car in each direction). In the larger states and in the Northern Territory, the tyranny of distance has a greater impact on those who live and work in remote locations.
I am sure there will be other unique conditions existing in other jurisdictions throughout the world, and so to me, one significant barrier to genealogy in the future will be to what degree the family history buff even knows to seek out the administrative rules and regulations that governed the actual creation of the official document they are looking at, at that future time.
Cheers, JM