In fact, Mary herself had to have been immaculately conceived, so that she would not bear the stain of Adam's sin -- because, apparently, sex itself befouls and stains your soul.

If I understand correctly, which is far from guaranteed...let's restart: I thought the Immaculate Conception of Mary was not a sex-free conception, but a regular with-sex conception made exceptional by the no-Original-Sin attribute.

From here:

Others think the Immaculate Conception means Mary was conceived "by the power of the Holy Spirit," in the way Jesus was, but that, too, is incorrect. The Immaculate Conception means that Mary, whose conception was brought about the normal way, was conceived without original sin or its stain—that’s what "immaculate" means: without stain.