Person A does not keep up with celebrities or popular entertainment. A knows that they exist, so I don't think sheltered is the right word.
Also, would it be a different word if A tried to forced herself to learn it?
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If you were to frame it more in a more affirmative sense of what the individual does embrace, rather than what he or she does not, you could use "elitist" or "aesthete" or perhaps even "philocalist" (OED " A lover of beautiful things.") - all of which convey a sense of fine discrimination. Perhaps that person might be a "paragon" (OED - "A person of outstanding merit; a person who serves as a model of some quality") because they transcend such petty temptations.
While something could certainly be constructed that would make sense to mean what you want, I think it's important to keep in mind the context of when such a phrase would be used. It sounds like you want something to use in everyday social conversation, which means that the answer must not only work but already be in common usage. I like "non-ephemeralist" from the comments, but it's not something that people actually say, so you'd have to follow it up by explaining what you mean in a lengthier form anyway.
I don't think there really is a specific word that fits. I might say something like "I don't follow pop culture," but that's probably overly broad - I do, for instance, follow the worlds of music and video games, which are certainly part of pop culture. You'd have to be more specific - "I don't follow celebrity gossip." Or, as a sort of metonymy, "I don't read tabloids."
Some of these are spoken slang:
I'm sorry, I've only now realized you're not looking for a judgmental term, but for something complimentary. Someone's already come up with "fad-proof", and that gave me this idea:
I construe it as a pun on fat-free. It might perhaps still be seen as derogatory, but this time not as directed toward you, but rather extending from you. There's a blog with that word:
According to the mass media, the current fads are all about being half-naked... but you don't have to sell your soul to be fashionable and look cute! Don't let anyone tell you that modesty is boring... or ugly, frumpy, dumpy, drab, or dull. Modesty is all about beauty. It is classic, timeless, and fad-free.