Name changed for this in case it gets messy.
I don't know if you've seen in the news but the singer Sam Smith came out as non-binary recently and has now asked that people use they/them pronouns with regard to them.
Absolutely not a problem with using those pronouns - I'm not a fan of theirs particularly so it's unlikely that they'll be cropping up that much in conversation anyway!
But - and I promise I am not being obtuse here, I am just old and slow but I am willing to learn 
- what exactly is non-binary? I just can't wrap my head around it. Surely the existence of non-binariness as a concept positions it as an alternative to an existing binary (i.e. men being macho and loving beer, women being all pink and girly and love wine) which I thought we all got over (or are meant to be getting over - sadly some people are very slow on the uptake!) anyway?
If I put on a pair of trousers or drink a pint or watch football I don't feel any less like a woman. I still feel like namechangeblah2019. How can you both refute the existence of a gender binary but also claim to be outside of it?
Please be kind to me - as I say I'm not implying they are wrong at all and if that is how they feel most comfortable being referred to then good on them and we should all respect that! I just want to learn as I currently feel like a right old fogey 