Okay, so let's unpack this.

1) Crossdressing doesn't make you transgender, nor does it make you gay. "The concept of otokonoko does not directly correspond to a particular sexual identity or gender identity. Otokonoko may be of any sexual orientation." This means that yes, otokonoko who aren't crossdressing men can and do exist, but I've yet to see (actually good) evidence that all "trap" anime characters are transgender, and not just almost exclusively crossdressing men. This ties into why it's translated as "trap", too; it's simply more accurate to the reality of the characters.

2) To whom, you ask? Why, anyone using their noodle, of course. A crossdressing man is not a trans woman; conflating the two is offensive to both groups, since you're trivializing being trans (the whole "trans*" thing does that, too, btw) and assuming that dressing like a girl makes you a girl.

Also, feminine men and masculine women aren't transgender either, not inherently, nor are the androgynous. Drag isn't transgender, either, although drag kings and queens are often gay.

You're still on this shit, dude?

You're flat out wrong, anyway:

"In contemporary Japanese culture, otokonoko (男の娘 Otoko no ko, "male daughter" or "male girl"), or otoko no musume, are men who cross-dress as women."

While "trap" isn't a fully accurate translation, it's closer and less offensive than "trans woman".