First of all, gender is not the same thing as sex, and transgender people have never said that it was. You assumed that they meant that, and misunderstood them based on your own lack of education on the topic. And that's okay. We don't all know everything, and frankly I wouldn't expect other cis people to understand the difference. Most of us have never had to think about it, especially if you're a heterosexual cis person. But now you've read this, and now you know, and now you're actively choosing to be an if you continue saying that transgender women are "men with dysphoria". 

And before you even start about how gender dysphoria is a mental illness, you should know that PTSD, anxiety, and depression are too, and those are commonly seen in the veteran population, so maybe you shouldn't speak poorly of people with mental illnesses unless you dislike veterans too.

Also, the treatment for gender dysphoria is...wait for it... transitioning your gender. I'm not making that up. People who went to medical school figured that out. Do you think you know more than a psychologist or psychiatrist? I don't think you do! 

Secondly, neither biological sex nor gender exist in a binary form. Androgen Insensitivity Syndrome. Klinefelter Syndrome. Translocation of the SRY gene. Genetic chimerism and mosaicism. There are as many intersex people as there are natural redheads. You can't pretend they don't exist just because it doesn't agree with your world view. Remember, facts don't care about your feelings, right? Y'all seem to only remember that when it's convenient for you. 

Gender is very nuanced and complex. I am a cis woman, but I don't define, view, or experience womanhood the same way that even my best friend does. We are both still women, though we are very different kinds of women; she has never treated me differently and I've never treated her differently. That's sisterhood. Something a lot of you have forgotten. 

In that same vein, I really don't understand why you would want to exclude your trans sisters. Trans women statistically do not commit sexual assaults like cis men do.

The data shows that if anything, trans women are more likely to be sexually or violently assaulted by cis men AND cis women. Trans women are not a threat to you, you have been lied to. Support your sisters, and stop blaming them for things that men do.