An update to this problem, in case someone else has the same issue.
The issue has nothing to do with zlib at all, it's problems with certain versions of libpng.
To get PixInsight working again, mask your libpng to stop versions >1.6.27 (this one currently works).
I'm still a bit puzzled why this is happening, as PixInsight ships with its own libpng in the bin/lib directory. However, at least I can get back to using PI under Linux again.