Just had the most ridicolous example of this ever.
Huayna Capac hogged SIX of the religions! I only just managed to grab Christianity.
I was on a very tiny isolated continent (Small enough that my OCC city had covered it fully with culture by the time I found the other civs...it had tons of great resources though so I couldn't complain...I was playing as Tokugawa).
So I find the others civs to find Huayna Capac...and discover that among his ten cities, 4 of them are holy cities! He has six religions!
So I check out the other continent....all...three civs? Wha? Anyway, they're all athiests running Theocracy (Zara, Mao and Churchill)! I then remember that the Native American and Egyptian Civs were wiped out around 200 AD or so!
Noticing that Zara, Mao, Huayna Capac and Churchill were all really behind in tech I started to build up a military. I first invaded Huayna Capac, using cannons and rifleman to attack and destroy, razing everything.
I then beelined Assembly Line for Infantry and Artillery for Artillery....
I then rebuilt my army and then proposed a resolution with the AP I had built long ago "declare war on the infidels"...
So I was at war with all three civs, who were all at war with each other and had been for centuries! I wiped them out pretty easily with my Aggressive/Protective Infantry against their Longbows and Cho Ko Nus..., winning a Conquest victory...anyway, this probably never would have been so easy without stupid HC religion hog.
It was simply far too easy to get rid of them all thanks to their constant warring...