This is a public service announcement? I don’t know. An announcement, anyway.
Start with the flatteningly obvious. Discrimination on the basis of sex, race, creed, national origin, age, weight, or sexual orientation is Not Okay. It’s not okay because it has no basis in fact. None of those characteristics is correlated in any way with anything that matters. (Yes, there is a boatload of excellent research supporting that point.) They are irrelevant. Discriminating on that basis does not work, in the sense of improving human life in any way.
Now continue with the equally obvious. Being transgender is also irrelevant to intelligence, kindness, or competence. Discriminating against transgender people in work, housing, education, or who can get married will also not improve anyone’s life in any way.
Let’s end with the one blindingly obvious difference. Sex does affect anything to do with biology, including medicine. Sex is a fact. Facts don’t care how you feel. Pretending otherwise changes exactly nothing. Hounding people for “transphobia” if they research the consequences of hormone therapy might get them fired , hounded , no platformed, or piled on  [the Times article is behind a paywall], but it won’t change the resulting sterility, loss of orgasm, osteoporosis, stroke, and so on  (pdf) through a list of side effects as long as your arm.
Sex also makes a difference in a world organized on a sexual caste system to exploit women’s labor and reproductive ability. Unlike biology, we can change society, and it would be great if we entered a new age of humankind where none of the gendered bullshit operated anymore.
We do not live in that world. Pretending otherwise does nothing but enable willful blindness to the injustice, and the people who suffer from that most immediately are women. Women can’t identify out of being raped or being underpaid. When those with a male developmental trajectory identify into women’s athletics and take the scholarships or money prizes, women can’t identify into a lifetime of enough testosterone to take the prizes back. Nor can female fetuses identify out of being aborted on the basis of their sex.
In this world it’s a fact that almost all (around 98%) of sexual violence is done by males . (Are we all sufficently tired of Not All Men? I hope so . The link is to an article about violent crime, but the same pattern holds for mere harassment. Very few perps can make a majority suffer.) Putting women in the bind of having to mindread male intentions in places where they undress  or can’t escape  is not a hallmark of tolerance. It’s a hallmark of assuming women don’t count. We all have a right to be, as the law puts it, secure in our persons. We get to do that without mindreading. The fact that men also target transpeople doesn’t make it women’s responsibility to compensate for the violence.
And that is the difference with other liberation movements. They struggled for their own civil rights. None of them tried to deprive others of what they wanted for themselves. Calling people who point these things out “transphobic” does not indicate virtuous tolerance for transpeople. It indicates a denial of facts on the order of flat earthers or creationists. It indicates a complete disregard for the human rights of women.