"Identifying as the opposite sex", then, boils down simply to a boy saying "I'm a girl" or a girl saying "I'm a boy". Is that it?
If so, my attitude - if not my child or one under my care - would be a silent shrug and perhaps a raised eyebrow. Same as "I'm cool" or "I'm a superhero" or "I'm a dinosaur".
My own child? Depends on context.
Following a discussion about gender identity in PSHE at school? -- I'd explain carefully and thoroughly, age-appropriately, the stupidity and incoherence of gender ideology. (Including, perhaps, an analysis of the history of the notion of 'identity' in such contexts. (Yes, I can do that age-appropriately.))
Just out of the blue, a throw-away remark? -- "Oh, yes? Good for you my love. And I'm the Queen of Sheba".
Or, well, and mutatis mutandis in other contexts. You get the idea.
Of course "identifying as the opposite sex" might mean something else. But if so, what?