The reference to the Arabian Nights reinforces the idea that the tale of the monkey’s paw seems like fantasy instead of reality.
One Thousand and One Nights or Arabian Nights contains stories that are magical and fantastical. These stories are set in a far-off, "exotic" place like the one where the paw comes from. To the Whites, India probably seems just as strange.
The reference to this book seems to make it clear that when they first wish on the paw, the Whites do not really know what they are doing. They think it is all a fantasy and nothing will actually happen. They are just having fun.
"Hold it up in your right hand, and wish aloud," said the Sargeant-Major, "But I warn you of the consequences."
"Sounds like the 'Arabian Nights'", said Mrs. White, as she rose and began to set the supper. "Don't you think you might wish for four pairs of hands for me."
Therefore, when the Sergeant-Major warns them about “consequences,” they do not actually take him seriously. He does tell them that the last person to wish on the paw used his third wish to wish for death, but they probably consider it just a story. It is a dark and stormy night, and their friend is telling ghost stories.
"If the tale about the monkey's paw is not more truthful than those he has been telling us," said Herbert, as the door closed behind their guest, just in time to catch the last train, "we shan't make much out of it."
Mr. White pays for the paw, but only a little. His friend does not want to take it. He just wants to be rid of the paw. They are probably thinking, why would someone give it to us if it is dangerous? As you can tell, they also believe that the other stories the soldier has been telling them are tall tales.
Of course, the Whites should have taken the paw seriously. It turns out to be real, and to have disastrous consequences. Either that, or there are quite a few coincidences in this story!