Saying you are transgender doesn't really mean anything. That could be anything from waking up once a week and feeling like you want to be something different, to going the full nine yards and getting reassignment surgery.
So, let's do this in a way that avoids all ambiguous wording.
People are one of the following, A, B, C, or D. D we'll save for later because it isn't based on "FEELINGS."
A has something that goes into something that B has. C doesn't have either capability.
Subcategories of A are:
A1: A's who feel like they should not be an A
And/or
A2: A's who want to be a B
A3: A's who want to be a C
A4: A's who used to be a B and have undergone genital mutilation so that they now are anatomically an A.
Vice versa for B.
If A has some secondary characteristics of B (man boobs for example), or B has some secondary characteristics of A (bearded ladies for example) that alone does not change whether they are A or B.
Most public bathrooms are designed to accommodate either A or B. There is equipment in those for A that B cannot use. However, most stores here have "Family" bathrooms that are available to A or B.
D is born ambiguous. Not their fault and it has nothing to do with feelings and they should be accommodated. Whether they have their "problem" fixed or want to live with it is their choice.
So which are you?