From the そうな・そうに grammar point:
つまらな そうな 話って聞きたくない。
I can understand that the つまらな そうな is modifying 話, so we have “boring talk,” and 聞きたくない is “don’t want to listen,” but I don’t see what the って is doing here. I know it can serve as a subject marker like は but in this case shouldn’t it be an を because the verb is transitive?
I don’t know, but maybe both are valid ways.
って and は mark topics, not grammatical subjects. They can replace both the subject marker が and the direct object marker を.
(Another way to think about it is that you can omit subjects and objects if they’re clear from context - 聞きたくない by itself is a complete statement. And then you can provide that context with a topic and make the statement into a comment on that topic. There is no explicit grammatical connection anymore, so the grammatical function of the part you omitted is not so important.)
NB: Verbs in the たい form work a lot like adjectives and can take a subject marked with が instead of a direct object marked with を. In most cases either can be used with no real difference in meaning.
I am not really sure but isn’t this casual quote って
I often think of は as “as for…”. 犬は大きいです。“As for the dog, it’s big.”
So if we interpret the って to be casual は in this case, it seems to me like it would be “As for a boring story, I don’t want to listen.” Or more naturally “I don’t want to hear a boring story.”