Cross-dress is a verb or action and it's definition is, “wear clothing typical of the opposite sex.” I am not going to get into the definition of sex but it typically categories denoting someone reproductive function, as in female or male.
So by proper word use, a transgender person can also cross dress; adjective adding clarity to the person denoting the action of cross dressing. The action of cross dressing typically would be a male (person) dressed (verb) in designated female garments or the opposite.
It is thinking like this that will fracture progress and will be used against us. Any combatant knows that with a united front, much can be accomplished. If you do not believe we are under attack, you do not understand the republican conservative agenda. The bullies targeted gays and failed, now they are coming for us, the transgender. Denying humanity to some is to deny it to all.
If we go off into factions, set against each other, then we give our enemies easy targets. "Cross dressers in the woman’s rest room" are not "men in the woman’s rest room". It is “gender dysphoria” plain and simple. To put forward this thinking, you provide license for discrimination, hate, bigotry and absurdity.
Thankfully a little further down the Quora discussion, Lynn Oddy, stated this:
There is a tendency to try and split trans people into transsexuals and cross-dressers as if they are completely unrelated - they aren’t, gender dysphoria drives both. It’s a matter of how strong the dysphoria is and what obstructions the individual has to transitioning.Let us be honest with ourselves. Likley all that read this blog are either transgender males or females and if we do not recognize that, our enemies using intimidation, will drive all of us back to the closet, one by one.