Thank you for taking the time to explain your thoughts on this. I've got a few points that I'd like to raise in response:
Typically I tell kids that nobody should tell them what they are,
Great! Although presumably you mean "how they should live their lives?" e.g. nobody should tell them that "this is what women should dress like, act like, do as a job etc". What they are is already pre-determined from the point of conception: they are human beings and are either male or female. From that start point, they should be free to embrace or reject the inevitable sex-based stereotypes that every society places on every child. Sadly every society has expectations and limitations that differ between girls and boys, even at a subconscious level e.g. when girls are born they are more likely to get lots of pink gifts compared to boys who are more likely to get blue gifts. From the word go, society tells us "this is what girls do" and "this is what boys do".
and they should speak to their health practioner and be fully educated on the risks and side effects of medical intervention
Why would you mention medical interventions to a child who is already vulnerable to believing that their lack of adherence to cultural expectations and/or lack of acceptance to submit to cultural limitations means they are "in the wrong body"? Surely the start point is that they are in exactly the right body and that it's totally ok to be whatever kind of boy/girl you want to be. Just by mentioning medical interventions, there is a bias from the start that their body might be wrong for them. They'll grab it with two hands as a possible answer for why they are confused/distressed if it's coming from an adult they trust.
I don't know any adult in my setting telling kids they can be any gender, just that it's ok if they are or they are questioning.
If any adult in your setting is sharing preferred pronouns, for example, they are already setting the scene that it's possible to be any "gender". That gender identity is important. That it's more important than what sex you are.
Typically the no to pronouns and name and haircut is delivered is in an unsupportive and needlessly fearful manner. It is atypical in my experience that caregivers want to watchful wait and are not doing so in an invalidating manner (the usual case) or harmful manner (less often now but was the normal 5 years ago.)
When my daughter experienced huge distress and confusion about whether or not she was meant to be a girl, I told her that she needed to keep using her normal pronouns while she worked through all of her thoughts on this. That it was important to stick with everything exactly as it is now and look at each thing that upset her on its own merits. Without introducing any bias whatsoever e.g. using sports bras (not binders) to help alleviate her distress about her breasts growing and the pill to alleviate her distress about her periods. I made it very clear that it was important that everything we did didn't change the status quo: that she is a female. Meanwhile, she desperately needed help with her mental health as she was struggling with all of it, plus bullying at school related to her autism. When she asked for puberty blockers to give her time to think we said no, because the NHS advised that there was an unknown impact on teenage brain development. We said we weren't happy with this kind of medical experimentation.
Here's what I was up against at the time: https://www.transgendertrend.com/teenage-gender-identity-crisis/
Does my approach sound invalidating? Or that I delivered it in an unhelpful, fearful manner?
I have a few detransitioned friends. I understand parental fears around the issue. I think if someone is worried about harm reduction, they need to weigh social transitioning carefully and not refuse it out of a place of "what if this leads to more"?
It is not a gateway drug.
The Cass Report explains very clearly that social transition is a "gateway drug". Obviously that's not the phrase that's used. Instead it is explained that social transition is "not a neutral act" and that it can bring in a bias which overshadows any other explanation for a child's distress, such as autism-related puberty distress, linked to sensory issues (breast development, periods) and distress about their body changing.