I would say that understanding the context Is essential, and that to describe social transitioning only as changing name and pronouns is overly simplistic in my opinion.
Transitioning is a process (it's recognised as such in the Equality Act).
A child who wears clothes associated with the other sex, but has no confusion about their sex/gender isn't socially transitioning, of course not. (FWIW, this describes me as a child, I hated "girls" clothes).
But if a child is expressing that they want to be the other sex, then wearing clothes traditionally associated with that sex could very well be the beginning of social transitioning.
I'm not saying they should be prevented from wearing such clothes necessarily. But that saying "crack on, let them wear what they like, nothing bad will happen" is potentially irresponsible / dangerous advice and not a reflection of reality.
For many DC who take this path, it has further developed into a medical transitioning with the significant health risks outlined in previous posts.
If one of my DC was expressing a desire to be the opposite sex, that would be my cue to get them and me appropriate support from an organisation that's not promoting gender ideology, and to explore with them what's going on, and how best to move forward, while making sure they know actually changing sex is impossible.
Whether the best approach for that individual child includes wearing clothes associated with the opposite sex or not depends on that child and what the wearing of such clothes means to them.
Blithely suggesting the child should cross dress within or outside the home and nothing bad could come of it is irresponsible given the huge risks associated with medical transition and the very real pressure from multiple sources online and at school that young gender non confirming DC will be under to "accept" a trans identity.
FWIW, when my DS started secondary he had long hair. He had no question about his gender, but he had to put up with other kids constantly asking if he was trans / a girl / wanted to be a girl. Luckily he falls into the category of DC who are confident and don't care what others think, but let's be honest here, being a pre-teen and teen is a tough time and few posess such confidence in the face of peer pressure. I certainly didn't, but luckily when I dressed "like a boy" it was seen as perfectly normal and no one asked me if I wanted to be one.
Sorry that's so long winded!
TL:DR - this is a complex issue, there's no one-size-fits-all approach. Youth medical transition seriously damages health and anything that could push a child towards it needs to be treated with extreme caution.