For the sportive challenge of AH, I try to come up with an really late PoD,
and hopefully, plausible alternate assumptions. At least, I neither erase
existing religions nor invent new ones.
Assume that Djingis Khan does not just let Muslim, Buddhist, and Christian missionaries dispute at his court, but have him embrace Buddhism.
If (second divergence assumption) the Mongol Empire last for a bit longer,
or control is a bit more intensive, we might derive
(i) a Buddhist Moscow,
(ii) Buddhist Turkic empires
from here, an further from the latter
(iii) a Buddhist Persia, Baluchistan and Mumbai.
Even if I can fill in the details for this sketch, it is obvious that it does not yet
do the trick. But it may be a starting point.
It remains to say that with this massive expansion of Buddhism,
local variants will of course develop or even split beyond recognition.
The main problem with this timeline sketch is the fact that the Mongols
did not exert that much cultural influence on their subdued peoples,
despite all their military strength.
And yes, as far as I understood the initial posting, "minority" is not meant in the sense
"fewer than half" or "fewer than each other indiviual group", but in the sence "splinter group".