"Zie" and it's 'possessive' form "zir" are used as pronouns (think "it" and "its" without the ugly connotations) when some combination of the following occur:
I nearly added something to the effect that the speaker/writer wants to overcome the patriarchal-based gender roles under which people have been suppressed for thousands of years, yadda-yadda-yadda, but that really still falls under point 3 because they don't know how to do so gracefully, and point 4 because they don't understand the root causes, thinking that spray-painting their language with clumsiness will excuse them.