We are opening up to the idea that binary conceptions of gender are unnecessarily rigid and don't correspond to the self-image of a great many people, and even that people's sense of their gender may not correspond to their biological sex. In this new world, a bland opposition between "he" and "she" seems increasingly antique, and even insulting, to many.
However, doing something about that is going to be a challenge. We are dealing not with merely giving new names to new things or actions, which is easy, but with using new pronouns, which is very hard.
This is hard because human cognition makes some parts of language more resistant to change than others. Nouns, verbs and adjectives, for example, are like software. It feels natural to add them, subtract them, revise them.
We expect them to change from era to era -- of course we now have blogs and twerking when we didn't 20 years ago; of course young people now call "fierce" what their equivalents long ago called "keen," "neat," "wicked," "rad," and so on. They are what linguists call open class words.
Pronouns, however, are closed class words. As shorthand for any thing or concept, pronouns are used so often and so unconsciously that they are more like hardware. A new object or practice is one thing -- but a new "you" or a new "him" or "her"?
It's harder to wrap our minds around changing something so cognitively fundamental, just as one does not pop up with new prepositions: You might wish there were a little word to indicate "on as in upside down on a ceiling, rather than on a wall or floor." But if you made one up it wouldn't catch on -- nouns and verbs are lightbulbs; prepositions are the wiring inside the walls.
Six-thousand years ago, in the ancestor of most of today's European languages on the Ukranian steppes, while most of the language would have seemed like Hittite to us (because it sort of was!), its speakers were using pronouns that sounded roughly like "me," "you," and "we" (not to mention the "tu" familiar from French and Spanish). That's how hardy pronouns are.
This is why previous attempts to fashion gender-neutral pronouns haven't caught on (believe it or not, there were once calls for the blend hesh!), and why as clever as today's "ze" is, its evolution from in-house tradition to society-wide acceptance will be slow at least, and possibly ill-fated. Bias alone will play its part, surely, but even without it, new pronouns require a mental effort analogous to conceiving dimensions beyond the third.
If anglophones are to accept new pronouns for new times, two things will be necessary. For example, the truth is that one thing that helps people change their pronoun usage is shame. For example, of all the "blackboard grammar" rules that English speakers are schooled in, such as that two negatives mean a positive or that one must say fewer books rather than less books, only one has truly caught on to the extent that it is part of the grammar actual people use comfortably. It is the rule stipulating that one must say "Billy and I went to the store" rather than "Billy and me," because me is "wrong" as a subject.
This is a rule no one imposed on English until a couple hundred years ago, and is unheard of in many other languages like French and Swedish. However, for better or for worse, it has been so successfully drilled into our heads as a mark of basic intelligence and propriety.
Now, I would hope that pronouns like "ze" would not be imposed with the knuckle-rapping and contemptuous indignation with which the Billy and I rule has been promulgated. However, there is room for presenting "ze" as a matter not of fashion, but of basic civility -- people must think of new pronouns as the proper thing to do, not as a stunt.
To the extent that societies change their pronoun usage, it tends to involve recasting old pronouns, or even expressions, into new functions. European languages like French, for example, use the plural "vous" to address a single person with respect. Spanish's respectful "usted" began as "your mercy," "vuestra merced," not as a brand new little word imposed by fiat. In this light, our own "they" could be handy as a new way to address people gender-neutrally. Many have called for exactly this.
And not just recently -- English speakers have been using "they" in the singular for eons. In starchy old "Vanity Fair," William Thackeray writes "A person can't help their birth." Today, we spontaneously use sentences such as "Tell each student they should hand in the paper on Tuesday." However, this is another of those things that we are told is a mark of ignorance because "they is plural." However, our new times may require that we get past that notion, which shouldn't be a problem because it has always been absurd.
After all, in French, vous "is plural," yet no one seems to mind. Once upon a time, you "was plural" while thou was used in the singular. Today, you "is" singular as well and no one bats an eye. In the same way, in our "hardware," "they" is both singular and plural. Our new conceptions of gender are a good time to get past the conservatism about singular "they."
The naysayers complain about the prospect of sentences like "They is upstairs," but this is a distraction: gender-neutral they should be used, as it has been forever, with plural verb forms: "They are upstairs" will mean that one person is upstairs as well as two or more. "But won't that be confusing?" one may ask -- upon which the answer is another question: When have you been confused as to whether "You are my favorite" referred to yourself or yourself and some other people? Context pulls a great deal of weight in how we communicate.
Assessing the prospects of new pronouns like ze and recast pronouns like they, my bet would be on they, in terms of the chances that, in 50 years, everybody is on board and on to the next controversy. What we do know, however, is that we are at a point where anglophones will need to accept some kind of change in how we use the language. Call it a teaching moment --language not only never stops changing, but could not.