She and my father haven't taken any special interest in my anime viewing over any other activity. I've only started recently, and I only NGE, SEL, and GITS on DVD, no merchandise or any other weeaboo shit. I've only explained it to them as another entertainment venue with its own unique style, and they haven't inquired any more about it.
My father used to watch Speedracer avidly when he was younger, and still has some posters and merchandise. Although I'm pretty sure both of my parents generally associate anime with Pokemon, Digimon, or Dragonball Z, but they nonetheless act indifferent to my hobby regardless of their opinions.
My father reads alot of fantasy novels, so I wouldn't see him being opposed to the idea if he were introduced to it properly. However he's fairly concerned with social image, so he probably wouldn't be able to get past outlook. As for my mother, she is quite narrow minded, so I wouldn't expect her to transcend the themes of the show and actually enjoy it's substamce, and she's more interested in shows like "The Bachelor" and "Survivor".
TL;DR version: They don't give a shit .