I've never really been persuaded by the 'facts are more important than feelings' statement. At best, it's an apples and oranges comparison in most cases. People don't typically claim they feel creationism is true, rather they take creationism as a fact. Similarly, the fact that I feel this way is nevertheless a fact, one which we take on good faith many times a day in person and online. If someone tells you they're angry, we're usually justified in believing that fact about their mental state. The degree to which we're skeptical of that claim is heavily influeneced in turn by epistemic trustworthiness and epistemic justice.

I think GP's point is that being or not being non-binary is unfalsifiable. I don't have a horse in that race, as I'm not sufficiently informed on the topic. However, it's important to note that (i) falsifiability is not the only reason to believe something and (ii) there is serious criticism of the idea that a statement must be falsifiable to be considered scientific.

I accept that someone is non-binary the same way that I accept that someone is a man or woman. I haven't had any issues with it so far, and it has the added bonus of making people feel validated, accepted, and comfortable around me, which is also a benefit to me in turn.