There is one thing I would hope for in your situation - since you mention there is continuing vulnerability around acceptance and rejection - is that a parent instils in their child the knowledge that while transphobia does exist, the vast majority of people who reject the claim that males can become female and females become male do not do so out of ignorance, bigotry or hate.
I'm afraid I don't think this is true and it's certainly not the impression most trans people get of the gender critical movement.
Firstly elements of the movement have been quite happy to stand alongside and work with open transphobes from the political religious right. These are people who think trans people are an abomination before God and deserve to burn in hell - that is literally what some of them think, that trans people deserve to be tortured for eternity. If you can stand alongside someone like that, if you can promote their organisations or give them feminist cover for their anti-trans activities then don't expect people to be sceptical if you calim not to be transphobic - you might not be but you are happy to tolerate it and propagate.
Secondly whilst it is claimed that many of the genuine concerns are rooted in the threat of male violence - in particular men accessing women's spaces, this seems to be a much more significant concern when it comes to trans people and not male identified males. There is no concern about male prison guards for example despite ample examples of horrifying abuse some of them have carried out. There is no pressure to ban male cleaners and maintenance workers from womens spaces, and yet it would surely be far easier for a man who wanted to abuse women to get a job as a toilet cleaner or caretaker, or pretend to be either, then pretend to be trans - and in fact some of the cases of hidden cameras that have emerged has been men doing exactly that. And whilst there may be those who are not keen on the idea of men becoming rape counsellor or training in women's healthcare, I've never seen anyone insinuate these men have some kind of sexual motive in the way I've seen it said of trans women in similar roles. I'm not denying that there are concerns about men, and with good reason, but it seems to me the concerns are often not just that someone might have been born physicially male but also that they are trans. That trans people, or trans women specifically are actually viewed as a greater threat than men which is why the FWR board spends far more time discussing the threat of the trans than the endemic male violence all women have to deal with everyday.
I think this is understandable and somewhat inevitable. There is a centuries old stigma against people born physically male who expressed any form of perceived femininty at all. For those of us a certain age we grew up in a culture awash with both transphobia and stigmatisation of feminine or effeminate men - and I don't mean just on TV or in films If Boy George had come into some of the pubs I started drinking in as a teenager he'd have been lucky to have made it out alive. That's the message society was giving out, that's what I learned, men who don't conform to the male gender deserve violence and will face violence. This is the legacy we are left with and I know myself I've had to battle the internalised transphobia it created within myself. I've seen very little self-reflection from GC activists on how this culture and social environment may have shaped their views and both conscious and unconscious prejudice - the attitude seems to be that just because some doesn't see themselves as a bigot or prejudiced then they can't possibly be that way - but it doesn't actually work that way.
Finally of course it's worth remembering that one of the foundational texts of gender critical feminism called for transsexuals to be morally mandated out of existence, and there are certainly those in the movement who still share that view. I suspect many GC people would really secretly just rather trans people didn't exist. Imagine how it feels to be told you should be morally mandated out of existence by one section of a political movement and then expected to believe there is no transphobia in that movement at the same time. I'm not a fan of using the phrase gas-lighting to describe situations outside of abusive personal relationships but surely that fits the bill.