The bigotry is more regarding the implication of harmful stereotypes against trans people as either transitory 'tom boys' or dangerous predators.
Its indeed interesting that those who purport to be against harmful stereotypes, certainly don't mind applying them when convenient.
"In an attempt to demonstrate her understanding of where transgender people are coming from, Rowling even says she too might have considered transitioning had the option been available to her as a teenager. “The allure of escaping womanhood would have been huge, “ she writes. “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.”
The belief that gender identity is a phase, a choice, or something that is influenced by other people is a stereotype that minimizes the struggles of anyone who experiences gender dysphoria. Transitioning isn’t easy but Rowling seems to be saying people can choose to transition on a whim simply because they think it’s more convenient to be one gender than another.
In her essay, Rowling goes on to reveal that she is a domestic and sexual abuse survivor and those experiences have made her even more focused on biology, “out of solidarity with the huge numbers of women who have histories like mine, who’ve been slurred as bigots for having concerns around single-sex spaces.”
Referring to the debate around public washrooms in particular, Rowling claims she’s concerned for the safety of cis women and girls. “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.”
Throughout her essay, Rowling talks about how easy it is for a biological man to become a woman in the eyes of the law and how potentially dangerous that could be for cis women. The fear that a large number of transgender women are just men who want to be able to use women-only spaces unchecked is a harmful stereotype that paints trans people as predators instead of just human beings who want to live their lives.
In her attempt to defend herself against the TERF label, Rowling just ended up providing more solid evidence that she is one. She works hard to disguise her views as feminism and genuine concern for the wellbeing of all women, but relies heavily on a number unsubstantiated opinions about trans people that the community has been fighting against for years. Rowling sees herself as highly educated on transgender issues but she still fails to see how her views—and her insistence on using her huge platform to promote them—are hurting transgender people."
https://inmagazine.ca/2020/06/j-k-rowlings-history-of-transphobia/