According to music supervisor, Nora Feld says The Duffer brothers asked her to find a song that resonates with Max, ""“Consequently, each of the prospective song placements in the initial scripts was tagged with the placeholder, ‘TBD Max song.’ From there, I made an effort to internally align myself with what the Duffers felt were the most important elements needed, and my own intuitive grasp of Max’s complex feelings.”
After choosing 'Running Up That Hill,' Feld says, “It immediately struck me with its deep chords of the possible connection to Max’s emotional struggles and took on more significance as Bush’s song marinated in my conscious awareness.”
The next obstacle was securing the rights to the song, which plays in a few episodes of Stranger Things, most explicitly in episode 4, "Dear Billy." Long story short, because of the usage, securing the song took longer than usual, as scene details, scripts, etc. were sent to Kate Bush for her approval.
It turns out that Bush was a fan of Stranger Things, and approved the song, even releasing a rare statement after the song became popular:
I've definitely heard Dua Lipa songs, but I couldn't name any off the top of my head.
