I can imagine it's annoying OP!
But not that uncommon. I consider myself a relatively sane, professional woman in my 40s. My teenage daughter and I have a show we really like, and we discuss the characters in a similar way.
And, now that I think about it, my mom and I have a couple of soap operas we follow, and our discussions about the characters in these are similar - in fact I sent her a couple of messages this morning saying similar, having watched tonight's episodes on ITVX as soon as I got up!
Your friend's only mistake (if it can even be called that) is in involving you in her chat when you don't share her interest.
Is there a thread about the show on here, for example? If so, maybe you could point her in the direction of it?
It's a fun, escapist thing to discuss characters in a show you enjoy with other fans - it may seem a bit childish but there is no harm in it, and it could be a good way for her to distract herself from stuff she is dealing with in real life.
BUT, that doesn't mean to say you have to humour her endlessly.
I think a kind thing to do might be to find and recommend somewhere online she could join discussions with other fans of the show?