I think at least a limited sense can be made of both suggestions, but Myers's suggestion is easier to see. Genealogically, at least, the sort of fantasy genre we get in the English-speaking world is arguably what Christianity does to paganism. It starts early -- think Beowulf or medieval adaptation of Greek and Roman stories -- and spreads through romances and fairy tales, and so on and so forth. For Anglophone fantasy is not just stories about fantastic things; much of it, perhaps the greater part of it, is making up pagan mythologies and legends, not for any religious reason, but simply for the enjoyment of it. One's reminded of Chesterton's lines in The Ballad of the White Horse:
"Ere the sad gods that made your gods
Saw their sad sunrise pass,
The White Horse of the White Horse Vale,
That you have left to darken and fail,
Was cut out of the grass.
"Therefore your end is on you,
Is on you and your kings,
Not for a fire in Ely fen,
Not that your gods are nine or ten,
But because it is only Christian men
Guard even heathen things."
Regardless of whether it's true elsewhere, this is virtually the motto of much of the monumental fantasy of the past century or so -- MacDonald, Chesterton himself, Lewis, Tolkien, and so forth. Many of the standard tropes of fantasy are at root paganism filtered through Christianity, even if they are further filtered through other things. Not just Anglo-Saxon mythology, as Kain suggests, but Icelandic, Norse, and Greco-Roman as well. Nothing about this requires that you be Christian in order to enjoy or write fantasy; but the fact that there is a fantasy genre is due, one might say, to Christians cutting the White Horse out of the grass long after it had ceased to have its original religious significance. Fantasy being as diverse as it is, there are certainly other strands. But whatever limitations are to be placed on it, one certainly can make sense of saying that fantasy is a Christian genre. Certainly Judaism, as such, is in opposition to paganism, and resists assimilating it, to a far greater degree than Christianity; it really does boggle the mind to think what a fantasy genre with purely Jewish roots could possibly be. Jewish folktales are possible, but as I noted above, people don't tell folktales as fantasy,and making the fantasy genre so broad that it includes folktales as one subgenre makes it a useless label -- it makes fantasy almost coextensive with storytelling, since completely nonfantastic stories are the minority, the unusual case, not the norm.
Further comments from D.G. Myers:
The Golem of Prague and the Jewish Aversion to Fantasy
The Difference Between Fantasy and Sci Fi