It appears that this person was subjected to homophobic abuse in their home country, but only identified as non binary once in the UK. They weren't actually persecuted for their non-binariness but for being gay.
There is a piece written by this person here:
www.crisis.org.uk/media/244227/howthelightgetsin_winter-2020-21.pdf
I went to court in November 2018 and revealed everything again. Sadly once again, the Judge didn’t look into all the details and she refused to grant me protection. According to the Judge, the incidents that I suffered were harassment rather than persecution, and they never gave me a reason why I wouldn’t be at risk in my country after all the evidence I presented. (Meaning they found it acceptable for me to be beaten by the police for my sexuality and abused in the streets.)
...
Physically, my appearance also changed. Without the fear of the attitudes shown to me in my home country, I felt confident to explore my gender identity. I let my hair grow and I started to define myself as non-binary, because I love the best of both of sides of the spectrum: I love gorgeous long blond hair, along with regular man clothes, and a touch of spice with my nail polish.
We tried to appeal with the Upper Tribunal, but unfortunately, they said there were not enough grounds for an appeal, so my case was completely closed. I felt hopeless, and couldn’t believe that my new life and gender identity could be ending. Fortunately, my solicitor found that my new appearance and gender identity evolution was actually new evidence that had never been taken into account
It seems from this that the homophobic abuse they suffered in El Salvador wasn't enough to be granted asylum in the UK, but once they identified as non binary, they were viewed differently.
And non binary for a male person appears to be long hair and nail polish, but for female people involves mastectomies and testosterone.
www.mumsnet.com/Talk/womens_rights/4119563-Elective-Mastectomies-for-the-Non-Binary