Turns out it was Joomla's fault, they accidentally reverted some routing changes in 3.8.4. Updating to Joomla 3.8.5 has fixed the issue and my users can use social login again:
Now you see why I wait 3 months to make Joomla changes.
Thanks for coming in to ferret the problem, although I had to change the "Yes" to a "No" again as at both my browser perspectives they didn't allow the Register/Login.
No worries as it appears to be working okay in the current state. Likely to be some local issue... happy to bimble along (an aviation expression) at the moment as it does the job. There may be something around the corner soon that reveals the problem.
Thanks again Alex. Highly recommend this product and your support.