The second link basically confirms what I suspected.
I don't see how your appeal to tradition is sufficient to justify your view.
Science generally accepts that the identities it discusses are nominalist and conditional. We humans create boundaries and classifications by grouping elements, but no such group or organization is objectively correct, some are just subjectively useful for particular purposes.
I'm not appealing to tradition, I'm arguing for it based on what I've understood about gender dysphoria or the concept of gender in general so far. To reiterate, gender dysphoria comes with all sorts of potential problems, like medication, surgeries, depression, discrimination etc. And that makes me believe that the best way to go about it for parents is to make sure (to a reasonable degree) that the child will not develop gender dysphoria and that the biological sex of the child will match the gender (a social construct, so we can influence it by controlling the environment). Unless you want to argue that what we've been doing up to this point actually makes gender dysphoria more common and the 'new way' suppresses it, or that I'm missing something important, I don't see any gaps in my reasoning.