Reporting from my home machine so system information here isn't useful
unfortunately, sorry. I can paste information from the Windows box I
experienced this on tomorrow.

To reproduce: On a Windows version of Emacs:

Evaluate (parse-time-string "2018-03-05")

A list of all nils is returned.

Removing the lexical-binding from parse-time.el solves the problem.
lexical-binding seems to have no effect on Linux.