I think there has to be a middle ground between some of the very polarised opinions here, because we're not dealing with an ideology, we're dealing with an actual child, at a time where hormones are rife and different influences are battling for control and emotions are incredibly high.
A lot of trans circles/communities, especially online, advocate for cutting off anyone who doesn't immediately and unquestioningly support. That's not healthy; there are reasons to cut family members out and I have absolutely done it myself, but it isn't healthy to cut off parents at such a young age for a reason like this - but you have to be aware that it's a possibility if those are their influences (I'm choosing to use they/them pronouns for your child, that's not me suggesting anyone is compelled to). Responding with some of the things suggested in this thread - total refusal to entertain the idea etc - will risk driving them further away.
There's a middle ground where you can support the child without supporting the path they're on. It might mean using they/them pronouns, if that's their biggest bugbear at the moment, but it leaves the door open to them hearing your concerns about more permanent choices down the road like surgery and hormones. Your concerns then are perceived as "my mum really cares about me and wants me to consider every option carefully", as opposed to "I need to cut my mum off because she's a bigot who won't even respect my pronouns". You may have to bite your tongue and grit your teeth as you do it, but tough love seldom works in these cases.
My perspective on this is as someone who previously felt I was non binary for around 3 years. I know there's a discussion in this thread about what non-binary is so I'll share my own experience - I became really uncomfortable with being referred to as "she", thinking of myself as a woman, having breasts etc. Not in a "oh that's boring I want something more spicy" way, it would genuinely upset me and to this day I have no idea why, it just felt incredibly wrong. Stereotypes, jobs and gender roles never played into it, I've always been a feminist, it was just a really deep discomfort with the idea of being a woman, but I felt exactly the same when I tried to think about myself with male pronouns etc. Non-binary felt a bit like a "catch-all", if I wasn't happy with woman or man it must be non-binary kind of thing.
One day I felt the same aversion to being referred to as "they". I went back to "she" and felt more comfortable (it still isn't 100% - the dentist asked me the other day if it was Miss or Mrs and I hate both of those and avoid giving a title wherever possible, but I settled on Ms 😅). To this day I have no idea what happened to my brain to make me feel this way (I mean, I have a fair idea - I was going through a traumatic time, I'm ND, I have a brain tumour so personality changes maybe?!) but that's why I err on a neutral stance - being supportive and encouraging the person to work through their feelings rather than trying to ignore or stifle them, but also warning against long term interventions. I am so glad I never went beyond a binder (which helped the body dysmorphia / dysphoria at the time).