This divide is so intense that there is very little common ground. There is little common ground even in the ways that the issue is conceptualized.
Sounds like a call for philosophy! Only, there's not much room for pure (a priori) ethical theory here. It's clear enough that we should prefer whatever will best serve the interests of the child, and help them to grow into a happy, well-adjusted adult. So it's really an empirical issue: what are the consequences of the two approaches likely to be? How burdensome is it to grow up transgendered, and how does this compare to Zucker's coercive therapy? (Might the cure be worse than the "disease"?)
Any remaining philosophical dispute lies more in what we might call the philosophy of psychiatry, concerning what counts as a mental "disorder", in contrast to "normal" human variation. Ehrensaft likens transgenderism to such "natural" variations as homosexuality, whereas Zucker compares it to racial identity disorder:
If a black kid walked into a therapist's office saying he was really white, the goal of pretty much any therapist out there would be to make him try to feel more comfortable being black. They would assume his mistaken beliefs were the product of a dysfunctional environment — a dysfunctional family or a dysfunctional cultural environment that led him or her to engage in this wrongheaded and dangerous fantasy. This is how Zucker sees gender-disordered kids. He sees these behaviors primarily as a product of dysfunction.
This strikes me as badly confused. Presumably a disorder is to be defined as that which tends to impede one's living a flourishing life. But that's an entirely forward-looking dispositional property; it does not matter how it came about, so this talk of "products of dysfunction" seems confused and irrelevant. Indeed, given a sensible forward-looking conception, it's not clear why adopting a different ethnicity must be a "disorder" at all. (It's not like losing a limb.)
Maybe the thought is that the expressed desire is actually just a symptom of some more deep-rooted unhappiness or self-loathing, which would survive the desired change and cause more psychological problems down the road? That would be an intrinsic or internal problem. Alternatively, one might think that the desire is problematic purely for extrinsic, situational reasons, e.g. if one lives in a community of Xs, the desire to be not-X might make it more difficult for you to flourish in this particular context. This appears to be at least part of Zucker's objection:
He explained that unless Carol and her husband helped the child to change his behavior, as Bradley grew older, he likely would be rejected by both peer groups. Boys would find his feminine interests unappealing. Girls would want more boyish boys. Bradley would be an outcast.
But there's nothing inherently wrong with outcasts. ('Misfit' is a relative term, remember!) The problem is with the society which doesn't accept or accommodate them. So it's really just the social stigma we should be worried about. But then I wonder why Zucker rejects the homosexuality analogy?
A final possibility is that he thinks it is a disorder in virtue of resting on false beliefs, or an inaccurate conception of the situation (in some sense). The black child who wants to be white may have internalized false beliefs about the inherent inferiority of blacks which explain (away) his preference. We may hold that preferences based on false beliefs lack normative weight and fail to qualify as 'true values', so it is better to change the misguided preference than to cater to it. But this normative principle isn't obviously true: we cater to poor taste and religious preferences all the time. Sometimes it's a better idea to just go with the flow rather than to insist on improving people.
But the point is moot because it doesn't seem that transgender-inclined children have false beliefs in any case. They don't, so far as I'm aware, believe that their birth sex is objectively "inferior" or anything like that. They just feel more drawn to the gender norms of the opposite sex. They're not making any error. So, again, I think Zucker's stance doesn't stand up to scrutiny.