I don't think so, or I hope not. I would like to think by now that gender and sex are separate enough - (although don't get me started on 'gender reveals').
Re your second part, they believe gender is a spectrum, but i dont think they believe the other. Transition is very, very rare, and again I can only speak for me, but its not something we see a lot of, especially as non binary takes off.
To try and get somehow connected with the OP, I think it is other people who make it a bigger deal. a 12 year old does not need the ins and outs of the types of things we are discussing.
If the neighbour's child wants to call himself James, wear trousers and a hoody and considers himself a boy, is that really so traumatising for this child to comprehend? Children are very, very accepting.
Someone I know once invited children in the class to quite an active party we were having. A child turned up with quite a significant disability, making access difficult.
They asked their child why they had mentioned it and the child's response was pretty much, "why would I?"
In life, we meet all sorts of different people. I can totally understand the worry with your own child, and your story has really touched me rod. Not having your wishes honoured is outrageous.
But if a parent chooses to let it ride its course, as I have seen it happen, and let the child figure it out, does it really have to be a big discussion in every household in the neighbourhood? Or is that us putting our opinions into things that really don't concern us? And no, I don't think it concerns the OP what another families' child is doing.