Some arguments that are flawed or refutable:
*Zelda's guise as Sheik is androgynous and not very masculine at all. Therefore she is not a transgender.
-Throughout OoT, she was referred to as he. The supplemental material that expands the story clear up that Zelda was given male features through magic in the transformation. Also a Sheik in etymological terms refers to a male leader in the Arabic and Islamic culture.
*Zelda only took up the identity of Sheik to conceal her identity, therefore she is not transgender.
-Zelda could have picked any disguise, yet she chose a male one. Why?
*Choosing a role as the opposite sex for social freedom does not make one a transgender.
-Lets break down the word, transgender.
trans
Etymology: Latin trans-, tra- across, beyond, through, so as to change, from trans across, beyond
gender
sex b : the behavioral, cultural, or psychological traits typically associated with one sex
By dressing up as a member of the opposite sex (gender), Zelda crossed (trans) the boundaries and that are considered normative roles for the sexes. That is transgender behavior. Many people live transgender lifestyles with better or other opportunities in mind.
*Zelda cross dresses only part of the time. She also identifies as a woman in other times and for the majority of the time. She does believe she is a man nor does she prefer to be one. This makes her not a transgender.
-Cross dressing, as I already explained previously is transgender activity. There are entire scales and categories of transgender behavoir.
Previously I broke down and pointed out that the word transgender, means crossing the gender norms or encompassing across it. Because Zelda lives a life as both a man and woman, that fits the description. It is also a misconception that all transgenders want to be physically a member of the opposite sex, or identified as one. Or for that matter believe nature made them the opposite gender by mistake. Most transgenders accept their natural born sex.
As someone who identifies as a LGBT, for years I disliked the labels put upon us or even identifying as a LGBT. I did not enjoy how because one engages in certain activity, has certain thoughts or displays certain traits that we automatically belong in a community. Deep down I personally believe that living things are beyond borders of sexual orientation, paraphilias, political lines, race, mental disorders and etc... However I have come to accept that the rest of the world uses these labels and I must adapt to get my point across.