I feel for you. Went through this exact same thing with my early teenage son some years ago, before I really knew about GC. It was intense because he was at risk of taking his life, so I had to find the right way of supporting him. It was truly horrendous, and I'm still not sure how we got through it. I was on 24 hour watch.
At the time, not much was said about GC at all, and we ended up going down the route of mermaids and the Tavistock. I just didn't know what to do, and it was in the news so much. Got as far as discussing puberty blockers. When it was mentioned that medication would affect his fertility, he decided he would stick with being male. Thank god he did! I just wish I knew then what I know now - but as a desperate single mum, I was doing what I could at the time.
He still struggles with his MH, but is mostly a happy, gay young man, of course he is. I suspect the issue was the daily abuse he endured at his school for his sexuality. It was relentless at times - and his desperation for it to stop - he wanted to "become" someone else if that makes sense.
So very thankful that we didn't go down that route. I'm so much more knowledgeable about this these days, and the tavistock is no more. For me, the process of the counselling he received made him realise what he is. And possibly saved his life.
I think what I'm saying, is that I understand your need to support whatever issue it is that your DS is going through, and not agreeing with him doesn't mean that you don't love him unconditionally. In fact, the opposite. It's because you love him that you want what is right for him.
I would have handled it very differently if it was today. I still regret the route we took and just thank my lucky stars it didn't become permanent.