Catholic Encyclopedia, cited above:

"This alleged popess is a pure figment of the imagination. In the fifteenth century, after the awakening of historical criticism, a few scholars like Aeneas Silvius (Epist., I, 30) and Platina (Vitae Pontificum, No. 106) saw the untenableness of the story."

So Pope Joan is untenable, but they still believe in a man born of a virgin, a water-walker who performs miracles, raises the dead and whose dad lives in the sky? Mmmm. Can't see the logic there, I'm afraid.