I don't know anyone who uses fiancee in a gendered way; all my engaged friends refer to their future husband/wife as their fiancee (though, granted, I'm probably not as old as many here who are already wed so I might just be out of the loop). Google's definition of fiancee seems to offer both wife-to-be and husband-to-be as synonyms as well, so I'm not really sure the parent's sneer is really valid in this case.
The word fiancé/fiancée is gendered. It is one of the few gendered words in English, as the gender was not dropped in taking it from French. Fiancé refers to the male. Fiancée refers to the female. They are pronounced exactly the same, which is why you have never heard it.
Words with semantic, but not grammatical, gender are not uncommon in English which lacks grammatical gender. Fiancé and fiancée are separate English words with different semantic gender, based on different grammatical gender forms from French (which, unlike English, does have grammatical gender.)
> Fiancé refers to the male. Fiancée refers to the female.
Actually, following French where male grammatical gender is used when the actual gender of the referent is unknown, fiancé is also the generic term.
The technicality here is that “fiancée” is historically female while “fiancé” is historically male. Same word, same pronunciation different suffix. Either way, nothing to get hung up about.