1) It's a shame to see a writer who has inspired many an 'underdog' in this world that you only have to be kind and considerate of others to be a hero, become a voice of oppression agains the ideals she wrote. Of course I'm talking about @jk_rowling
2) To begin, this is not a suppression of your opinion. You have the right to it, but that does not protect you from being critiqued on that opinion. The same goes for anyone. People take umbridge with your opinion because it weighs heavily on many people's lives.
3) Given your position, that opinion goes a long way and can influence many people: both those is directly affects, and those it doesn't. Those unaffected may take your word as gospel, and believe trans people are lesser than they and treat them as such.
4) Those who are directly affected (trans people) may also take your word very seriously and believe there is something very wrong with them. Coming from someone they idolise, someone with a huge sphere of influence, may cause stress, mental breakdowns, or cases of self-harm.
5) Now my opinion on the matter is quite clear: trans women are women, trans men are men. But my opinion is a drop in a bucket. Yours is a bucket all of its own. You don't seem to understand the weight you carry in that regard, and are weirdly surprised by the splash back too.
6) And to defend your position/opinion on trans rights by making it a feminist issue is very rich. Gender cannot be both your shield, your swore, and the hill you die on. Saying your opinion on what qualifies a gender is being contested because you're a woman is hypocritical.
7) You've infringed these people's rights to be the gender they know they are, so of course they are going to take issue with it. I don't speak for the clearly inappropriate responses of course, but surely you can understand that those people do not represent the whole.
8) We could argue mental health, biological, or social angles of the trans right debate, but that's not what this thread is about. For someone who cares about debating, you seem eager to write off all opposition to your views as bias, regardless of the educated counterpoints.