I am an INTP who would classify as HSP and I have no fear of heights, except for healthy wariness. I actually love heights.
I am the sort of person who would climb a tree in a windstorm if I could gauge that I wouldn't be knocked out of the tree; I'd climb a tree to the highest point where I still felt the branches wouldn't break; I love scenic views; I sit with my feet dangling over cliffs; I walk on open-grate bridges without a problem and enjoy looking off; I love looking out the windows in an airplane; if I had my life to live over again, I would practice alpine climbing. It's not heedlessness, it's just being locked into the world enough that I can feel where the limits between safe and dangerosu are rather than just freaking out because of what would happen if I fell; no, it's about, "Would I reasonably fall off or not?"
I'm not scared of cars because of what would happen if I hit a tree, am I? Well, I'm not scared of heights just because of what could happen if I fell, if I'm behaving in a way where I am still safe.
My former MIL (a non-hsp ISFJ) was terrified of heights and I used to drive her batty because I had no fear of them; she couldn't watch me.
Hmm, everyone who got HSP is voting fearful of heights...
uh... no.