Santa vs Jesus described itself as the "battle for the most believers and ultimately [to] rule Christmas".
The game was created through a crowd funding initiative where members of the public donated more than £7,000 to get the idea off the ground.
It is being sold on online store Amazon but critics are demanding the company delist it.
"Absolutely shocking and blasphemous to use the good name of our Saviour to promote family fun," said one.
It was "wholly unacceptable and offensive," they added.
One shopper, identified as Rev Elaine, said: "How cheap and nasty to corrupt the beauty and meaning of Christmas in this way."
Another questioned if a board game would be made poking fun at any other religion.
However another customer said: "Haven't played it yet but had a quick look through. Looks enormous fun. I am a Christian and am not the least offended by anything I saw. Take it in the spirit it is meant to be played."
Others described it as "really, really funny" and an "epic Christmas party" game.
