Yes I have a child who say they are non binary, although childhood has been fairly gender conforming (whatever that means!)
I initially found it very stressful and felt as if I was grieving for the daughter I thought I'd lost. Things have calmed down since then. My child doesn't have any body dysmorphia and isn't changing name so that makes things somewhat 'easier'.
Things I've learned:
Professionals are all too quick to try and push you down a trans route, regularly mentioning mermaids and tavistock far too quickly. Balance out the advice from mermaids with parenting forums on the matter (who almost always say avoid mermaids - I think it depends on your own situation though and I do not feel that charity is right for us at the moment).
I use the 'DC is awaiting diagnosis for ASD - we need to wait and see because if that is diagnosed, child needs to understand what that means before we go down a route that could actually just be a very usual ASD feeling of not feeling 'gendered'' - so far, this has worked with school/CAMHS holding off. To be fair though, my DC is not distressed about it so I don't think there's a need for intervention at this stage.
Some adjustments at home - no gendered birthday cards; hurts but fine. Short hair - no problem with this at all and showed my 80s school photo of all girls having short hair then; hair length has no bearing on whether you are a woman or not. I really don't want to change pronouns yet until ASD position known, it seems so final, DC has agreed that's OK for now. I try and avoid where I can using name.
Assured DC that if they choose to live adult life as non-binary, will accept it, however, as ASD not yet diagnosed (late discovery) not willing to make all changes until that has been explored and understood i.e. is this just ASD feelings or is it more?
Honestly? I hope she accepts herself as an ASD female when the time comes. As it can be common for ASD children may not have an entirely hetero attitude to sexuality it may just be that she's gay or bi (or pan as they call it now). I feel 'lucky' that so far, things have calmed and the changes have not gone too far. Obviously that may all change in the future but I am trying not to think about that.
I was at an event where a leading ASD in females expert said that studies were ongoing about gender identity in females with ASD so she couldn't say too much more on that BUT also said to be cautious with anyone claiming they do know. I have to say that the awaiting ASD diagnosis has helped no end with professionals and my child to keep things low key. Goodness knows what will happen after the ADOS is finally done.
Very best of luck.