1) Non-binary as a concept on so many levels can actually be harmful, including harmful to trans people due to it creating a position where it's not actually affirming their new gender identity but creating an undefined 3rd position.
But, contrarily to what you say, sexual identity is not binary, it's not the reductive XX vs XY opposition that we learn at school. Genetic reality is a more complex continuum, and that's why, for instance, intersex people are born with male and female characteristics. Unfortunately, we live in a conceptally poor culture that has mythified and entrenched binary oppositions (other cultures leave room for a 3rd sex even if, itself, is also a reductive catch-all), and the result of that is the guesswork of surgeons tasked with physically cutting out at birth the bits that don't fit an arbitrarily assigned category.
The non-binary aspect of sex is a simply a thing. So, who its aknowledgment annoys and why (be them cis or trans) is simply not a factor. I know that a lot of people love classifying themselves, it gives them a sense of self, a validating administrative existence. But that's a symbolic, pilosophical choice. Reality doesn't care. And no matter how uncomfortable, a lot of people stay in the no-man's-land between categories (or overlap them) in many domains of life, not just sexual identity. Denying it just to make our arbitrary conceptual tiles look cleaner, and to further mythologize its adequacy with nature, is just sacrificing people for a pointless misconception.
And that's just biological sex, don't get me started on gender. Gender is the cultural identity wrapping over that, but damn, does its over-simplification also imposes its share of mismatch.
2) There's a difference between don't be Transphobic / homophobic and making it out to be something special (which is therefore not normalising it). Certain topics especially with young children can be....... not the best thing to suddenly have a character on about especially kids at certain ages who like to copy said characters to an extent.
There is no big deal about that. Children book also present secret royalty, foreign religions, cops and robbers, anthropomorphic animals, all sorts of identities that kids can "copy" for a while. What matters is if they emulate decent people (models) or creeps (counter-models). Not if they emulate muslims, kingdom heirs, martians or non-binaries. It's not even a big deal after puberty, when it comes to relationships. They should be free to identify with what's most comfortable for them, and experience the most comfortable love to them.
It only becomes a big deal when transitional surgery is at stake, because we're unfortunately far from having a magic pill or sci-fi ray allowing us to switch back and forth between gendered bodies. It's a tough procedure, and a big decision. But hey, it's just one amongst so many. Life is like that - accepting or refusing a one-time job opportunity, moving country, marrying and having children with the right or wrong person, all of these are tough freedoms of choice with the occasional irreparable wrong one, and yet we still don't legally deny people's agency when it comes to them.
The stake of treating like existing, "normal" (morally if not statistically) human beings the people who fall between our traditional cultural categories is much bigger than these concerns. These concerns are overblown by the (understandable) sense of cognitive scandal that the most conservative people experience ("but but but I have always been taught that it's either male or female, and that not conforming to this was shameful"). Now of course, we're living through an awkward readjustment to a fairly recent public awareness, and this implies some hesitations (on how exactly to assess gender mismatch claims, for instance). But we're very very far from the causes of melodrama and moral panic that conservatives try to lather.