I think INFP, based on numerous interviews and her art (especially her lyrics). Overall, I get an impression of abstract Feeling (Fi) and concrete iNtuition (Ne) rather than NiFe. Her style of expression seems so different from most INFJ musicians; her imagination seems expansive, whimsical, and pulling things in from a hundred different directions, playing off of them and making them uniquely hers by processing them through Fi and giving them vibrant and idiosyncratic emotional color. INFJ imagination is more heavily abstracted/removed from its input, and in my experience comes across as less whimsical and playful and more focused and intense. The links from external input to internal vision are much harder to trace.
You'll find that INFJ music tends to have a focus not only on people, but also some overarching idea, web of concepts, connecting people to the universe, cosmos, and how we all play a role within this massive web and how we could avert natural disasters (ex. Muse's song Unsustainable).
Yeah, I thought about something like this: how INFP art, while it can be tremendously imaginative, tends to focus more exclusively on the human realm* and INFJ art tends to have more of a transcendental/universal aspect*, and this is partially why I got the impression of Kate as an INFP.
*In general, not always.
INFPs sometimes write about existential or societal issues as well, but compared to INFJ writing there's less of an aerial view of the issues themselves and how they affect humanity at large; the INFP approach is more personal and more about the effects of those issues on an individual (sometimes the songwriter herself) who can be viewed as a microcosm. The personal approach seems more like Kate Bush's writing style to me.
I find most INFP music to be alternately playful and emotionally intense/moody. (4w5 leans more toward the heavy side; 4w3 is pretty balanced, and 9w1 is lighter/airier.) I perceive most INFJ music as more serious and showing a more intense vision, but as also containing less intense emotion.
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Some general patterns I've seen in INFJ vs. INFP writing (there are always exceptions):
I agree with the people who said that writing songs from a character's point of view is more common among INFJs, but INFP songwriters do it too sometimes - Tori Amos and Kurt Cobain come to mind. The difference is that INFJs tend to use a macrocosmic approach - they often write characters as symbols that represent either aspects of humanity (that link and define
people, as opposed to what defines a particular individual) or universal concepts that relate to the human condition. If they write from the point of view of an already-existent character or person, they normally are attracted to that story/person because they find some symbolic significance or illustration of universal truth in them. INFPs don't usually turn characters into symbols - concepts aren't the point; the character's story/experience is. Instead of linking a character outward to something cosmic or to humanity in general, INFPs "link in" by using their own complex feelings as a map to empathize with and dig deeply into the character. This can lead to insights about what's universally human as well, but it's more like putting a magnifying glass over a tiny section of humanity that most people can find in themselves, rather than taking patterns perceived in humanity in general and transplanting them into a character. Also, when INFPs write about a character or person that already exists, they normally choose them because they find a strong personal/empathic pull or fascination towards them, or they can relate to them somehow (not necessarily in a situational or concrete way).
Even though writing such a large percentage of one's songs from the point of view of a character is more common for an INFJ songwriter, Kate's writing style still strikes me as more INFP. This is mostly based on my subjective interpretations of her work though; someone else might view it differently. I haven't heard her talk much about her motivations for choosing certain characters and the details about how she writes them, so the INFP typing is still tentative.