You're allowed to have an opinion, but you should know it's a bad one. For one it's misinformed; Non-binary isn't about sexual orientation, it's about gender identity. It means "I don't see myself as a either a man or a woman." It has nothing to do with sexual preference.

Two, your analogy needs some work. It'd be more like if someone asked an architect "are you an artist or an engineer?" but the architect says "well, I'm kind of both" and the person refuses to believe that's even possible.

Or if you told a family member you're a software developer and they go "Oh, you work with computers? Can you help me fix my laptop's broken screen." When you try to explain to them that you can't, they get angry because "is a computer so you should be able to fix it right? Stop being so pretentious talking about servers and sequels and just help me." The problem isn't that they don't understand what you are, it's that they assume to know based on their simplistic, surface level understanding. And then they get mad at you for not conforming to their ignorant assumptions.

And lastly, if you actually just don't care about any of this, then shut the hell up and move on. Don't say you don't care and immediately start bitching about something you don't understand. You can keep your head buried in the sand, but fucking leave it there.