On my last day at Worldon in San Antonio, I listened to Lou Anders give his workshop on taking tips from screenwriting and applying them to novels. Although I took copious notes, instead of summarizing them, I’ll give his surprising way of defining antagonists. The antagonist is not necessarily the villain, but is the person who puts obstacles in front of the protagonist.
In Casablanca, Rick is the protagonist, but the Germans are not the antagonists. The antagonist is Laszlo, Ilsa’s husband, because he is the one who puts roadblocks in Rick’s way. Laszlo is undoubtedly a good guy, so in the end Rick deals with him and with his love interest Ilsa in a way that is appropriate.
In Star Trek II: The Wrath of Khan, Khan is not the antagonist, at least not for much of the movie. For much of the movie Lieutenant Saavik is the antagonist, quoting regulations against Kirk.
This different way of looking at the antagonist is helpful, especially when the villain is not interacting with the protagonist for much of the story.
Speaking of Star Trek, this woman who had a couple of young children with her wore the uniform sheath from the old Star Trek, even though the temperature could be over 100 degrees in San Antonio.