Chesterton's fence and similar Burkean arguments are generally a reasonable position. But in this case, we know:

1) There are people who desire to do things that are not acceptable within their gender roles (i.e. cross-dressing)
2) Internalizing gender narratives makes those people miserable
3) Those people (as a group) are not more likely to engage in unacceptable behaviors (i.e. molest children)
4) Prior changes to gender and other social norms have occurred without society falling apart
5) Plausible arguments exist that those changes were net benefits for society (preventing Condoleezza Rice or Hilary Clinton from being Secretary of State is wasting talent)

In short, there is obvious and significant suffering that these changes could plausibly alleviate. Comparing these changes to similar changes suggests the downside risks are low. Even Burke acknowledged that change was sometimes necessary - otherwise Burkean conservatism becomes a fully general counter-argument.