“I support trans people’s rights to live as they want, but I value womanhood and take pride in my womanhood. As such, I want trans people to live as they want, but I want to keep the idea of womanhood separate because I value it as a space for women.”

If that was what she was saying it'd be fine. You would likely need to do a little more than 5 minutes of searching to understand what all the commotion is about but I might be able to provide some context that would help. If you actually want to read all of this.

Let's take the essay she wrote on her website.

For people who don’t know: last December I tweeted my support for Maya Forstater, a tax specialist who’d lost her job for what were deemed ‘transphobic’ tweets. She took her case to an employment tribunal, asking the judge to rule on whether a philosophical belief that sex is determined by biology is protected in law. Judge Tayler ruled that it wasn’t.

You can read that court case ruling and see examples of what comments Maya made, through tweets, slack, and otherwise. JK puts transphobic in quotes and words her comment in a way that is implying that she does not agree with that label. This example from the document is pretty on the nose though:

I believe that it is impossible to change sex or to lose your sex. Girls grow up to be women. Boys grow up to be men. No change of clothes or hairstyle, no plastic surgery, no accident or illness, no course of hormones, no force of will or social conditioning, no declaration can turn a female person into a male, or a male person into a female.

Then the essay says:

Months later, I compounded my accidental ‘like’ crime by following Magdalen Berns on Twitter. Magdalen was an immensely brave young feminist and lesbian who was dying of an aggressive brain tumour. I followed her because I wanted to contact her directly, which I succeeded in doing. However, as Magdalen was a great believer in the importance of biological sex, and didn’t believe lesbians should be called bigots for not dating trans women with penises, dots were joined in the heads of twitter trans activists, and the level of social media abuse increased.

Magdalen Berns wasn't "a great believer in the importance of biological sex", she was openly transphobic and compared it to blackface.

So twice JK is defending clearly transphobic people and downplaying it to things like, oh they just tweeted something or just believed in biological sex (whatever that means) and were canceled by activists online.

Then later in the essay she says:

Most people probably aren’t aware – I certainly wasn’t, until I started researching this issue properly – that ten years ago, the majority of people wanting to transition to the opposite sex were male. That ratio has now reversed. The UK has experienced a 4400% increase in girls being referred for transitioning treatment. Autistic girls are hugely overrepresented in their numbers.

That does happen when there's an increase in awareness, access, and acceptance of something.

The same phenomenon has been seen in the US. In 2018, American physician and researcher Lisa Littman set out to explore it. In an interview, she said:

‘Parents online were describing a very unusual pattern of transgender-identification where multiple friends and even entire friend groups became transgender-identified at the same time. I would have been remiss had I not considered social contagion and peer influences as potential factors.’

Littman mentioned Tumblr, Reddit, Instagram and YouTube as contributing factors to Rapid Onset Gender Dysphoria, where she believes that in the realm of transgender identification ‘youth have created particularly insular echo chambers.’

Her paper caused a furore. She was accused of bias and of spreading misinformation about transgender people, subjected to a tsunami of abuse and a concerted campaign to discredit both her and her work. The journal took the paper offline and re-reviewed it before republishing it. However, her career took a similar hit to that suffered by Maya Forstater. Lisa Littman had dared challenge one of the central tenets of trans activism, which is that a person’s gender identity is innate, like sexual orientation. Nobody, the activists insisted, could ever be persuaded into being trans.

With this, JK is pushing the idea that trans people (especially teens) are confused, or are just following a trend, or being persuaded to be trans. Rapid Onset Gender Dysphoria is a made up term implying people wake up one day and decide to be trans, minimizing what is, for many trans people, years of hiding their identity from their family and friends. The study she's mentioning from Lisa Littman did not involve trans people, and is actually only a survey of 256 parents of trans people. Here's a bit from the paper:

[...] Most of the parents (80.9%) answered affirmatively that their child’s announcement of being transgender came “out of the blue without significant prior evidence of gender dysphoria.” Respondents were asked to pinpoint a time when their child seemed not at all gender dysphoric and to estimate the length of time between that point and their child’s announcement of a transgender-identity. Almost a third of respondents (32.4%) noted that their child did not seem gender dysphoric when they made their announcement and 26.0% said the length of time from not seeming gender dysphoric to announcing a transgender identity was between less than a week to three months. [...]”

So she's basing this entire section of her essay on a survey of 256 parents from various groups online like the "Parents of transgender children" facebook group and making it seem like there's a trend of teens, again, waking up one day and deciding to be trans. This "republishing" that JK mentions made corrections to the paper and included an apology from the editor. But, JK represents it as just outrage from activists online.

Then she pulls out this classic:

[...] The more of their accounts of gender dysphoria I’ve read, with their insightful descriptions of anxiety, dissociation, eating disorders, self-harm and self-hatred, the more I’ve wondered whether, if I’d been born 30 years later, I too might have tried to transition. The allure of escaping womanhood would have been huge. I struggled with severe OCD as a teenager. If I’d found community and sympathy online that I couldn’t find in my immediate environment, I believe I could have been persuaded to turn myself into the son my father had openly said he’d have preferred.

No, you probably wouldn't have tried to transition to escape womanhood. Being a Trans Man is not some vacation from the struggles of being a woman. She even acknowledges some of their struggles later.

I want to be very clear here: I know transition will be a solution for some gender dysphoric people, I’m also aware through extensive research that studies have consistently shown that between 60–90% of gender dysphoric teens will grow out of their dysphoria

I'm going to quote another site I read for this one:

Some studies do show that prepubescent children showing signs of Gender Dysphoria will likely “grow out of it” (though these studies have had their methods, data and analysis called into question), they also show that if Gender Dysphoria persists into adolescence that “it is almost certainly permanent”.

Then the meat and potatoes of this, natal women's safety:

So I want trans women to be safe. At the same time, I do not want to make natal girls and women less safe. When you throw open the doors of bathrooms and changing rooms to any man who believes or feels he’s a woman — and, as I’ve said, gender confirmation certificates may now be granted without any need for surgery or hormones — then you open the door to any and all men who wish to come inside. That is the simple truth.

Trans women have been using women's spaces for decades, this certificate process makes no difference. If this was going to be an issue it would've already been one by now. Instead she's fearmongering this idea that Men will all of a sudden with no other effort just claim to be a woman and start sexually assaulting women. The truth is trans women face many of the same threats of sexual violence and in JKs world they would have to use the same facilities as men.

This is, in part, why she's receiving all of the hate. Death threats and all of that are over the top but that's not an issue that's specific to her, people suck. However, despite the polite way she words everything, she defends other transphobic people and is pushing to deny trans people rights and healthcare in the interest of Women's safety using unfounded claims based on misinformation and bad data.