I disagree. Parents tend to come around and eventually accept their kids. Bringing her in to your home would drive wedges between them and you and your then former friend.
"Mind your own business and you'll find it's a full-time job.........
Agree with part 1, reject part 2. However, part 1 depends somewhat on how much time this friend has already sat this EarTh SHatTErInG!!!!!!! news that his kid doesn’t prefer the standard binary gender social constructs.
About how old is Claire? Focus your response on them, particularly if you really do know them. DO NOT debunk the gender phobia, nor your friend’s Wile E. Coyote-like inability to avoid the very obvious disinformation and misinformation rabbit holes. There is a small chance he remains comically suspended above the hole, but your friend isn’t the priority, now, and will likely respond to the overwhelming evidence that he’s been duped by entrenching further (his emails contains some of the more doltish mis/disinformation, indicating he may already be terminal). You're not likely to shift his perspective, on much of anything, but give it a go, for Claire, even if the potential shift is slight.
My response would be something to the effect of “I’ve always known Claire to be [insert affirming and pride inducing characteristics and experiences - expand, expand]. From my understanding, I imagine Claire had to muster quite a lot of courage to reveal this part of herself/themselves (I debate about the misgendering- I tend to think you should, at this time, to keep your friend on the line). At the same time, I can only imagine how this feels as a parent of a kid whom you love deeply and for whom you want the absolute best, but suddenly find yourself profoundly conflicted by something as socially prominent, and hammered in the media, as gender.”
I’d then say something to the effect of:
“I too have experienced confusion and dissonance, at times, with the evolution of gender terms and norming. Middle-age is a weird and disorienting space. The world changes with each generation, often at dizzying speed, and I find it can be hard to keep up. At times, I’ve felt like the bad guy for not understanding what’s important to younger generations; though, I’ve appreciated their eagerness to educate and express themselves, when I’ve approached with neutral curiosity. In my experience with Claire, she is [more plaudits re thoughtfulness, courage, independence etc. maybe throw in a commonly shared anecdote that friend can reflect fondly upon]. She’s a great kid, and I’m eager to be here for her, [insert spouse, if you think appropriate], and you. If you’re willing, I’d appreciate a chance to talk things out over the phone or lunch; writing “thoughtful” emails takes me so much damn time! Best, my friend.”
Some of this might not apply if Claire is quite young and/or a bit of a pill, but you’re a smart person with the ability to adjust language, as needed. My focus would be singularly on trying to focus on empathy within the family and between you and friend - it’s the
only inroad that eventually leads this situation to a healthy ending.
ETA: I initially missed that you may be older than I presumed and maybe not as communicative with friend - which would change my language, but not my overall aim.