I disagree.
The issue in your initial post is that you are hitching the non-binary wagon to the legitimate mental distress of gay men and lesbians. It reads as tactical laundering and opportunistic co-opting of a distinct struggle.
Homophobia (targeting people for their immutable, sex-based orientation) is fundamentally different from scepticism or mockery directed at individuals announcing a personal identity based on clothing, personality, or vague discontent with gender stereotypes. The former is rooted in material reality and centuries of persecution, whilst the latter is a contemporary aesthetic ideology, adopted voluntarily and maintained through performance and declaration. These experiences are simply not the same. 'Non-binary' is a self-ascribed label, not an innate or inescapable condition. The so-called unsupportive environments non-binary people may encounter are simply not on par with the entrenched hostility that gay men and women have historically had to navigate.
Failing to support gay and lesbian people has meant punishing them for what they cannot change. It's unquestionably a societal moral failing.
Refusing to endorse non-binary identity claims is not in the same category, and pretending otherwise trivialises the real thing. It's akin to a Scientologist claiming to be oppressed because nobody around them believes nor takes the threat of Xenu seriously.
It's disingenuous (and frankly lazy) to generalise those who are critical of non-binary identities as de facto homophobes. You're welcome to argue the perceived hardships of non-binary people, but do so under their own placard, not by grafting their cause onto a history that is not theirs.