Hi, I've gotten this same error twice in the past few months.  I'm currently running ArcGIS 10.5 (recently upgraded from 10.4) on a Windows 2012R server.  I'm also connected to a feature service sourced from a PostgreSQL 9.5 (upgraded from 9.3, I think, when I upgraded ArcGIS) geodatabase (gDB) on a CentOS 7 server.  Here are the actions which caused the same error under both ArcGIS/Postgres versions: 

1. I had ArcMap open (I wasn't connected to the Postgres gDB this time; I don't remember if I was connected the last time).
2. I tried to restart the Postgres service after making a change to its pg_hba.conf, but got an error about the lock file postmaster.pid already existing.  
3. I closed ArcMap.  
4. I tried restarting Postgres again; I was successful.  
5. I reopened ArcMap and tried to connect to the Postgres gDB, but got an error (attached) about how ArcMap couldn't load the st_geometry.so file (I'd had no trouble connecting to the gDB before getting this error).  
6. On the CentOS server, I deleted then recopied the exact same st_geometry.so file from the Windows server onto the CentOS server that was in place before the error.  
7. I tried reconnecting to the gDB in ArcMap; I was successful.  

Any ideas why I get this st_geometry.so file error?  I'd restarted the Postgres successfully many times after modifying its pg_hba.conf file; thankfully this error has only happened twice so far.