You mean besides the fact that a dozen countries have had it for years without major issues, which surely TERFs would be frantically promoting if they existed?
well, the govt of Argentina did a study and found that there was no rise in violence against women in the first decade of self-ID and that there was exactly one (1) trans woman convicted of sexual assault between 2012, when it was instituted, and 2019 (in b4 someone says convictions hugely underreport actual instances of sexual assault: sure. you're still going from up one (1)).
And, when the UN's Independent Expert on protection against violence and discrimination based on gender identity and sexual orientation (mouthful of a title, if specific) testified before Scottish parliament on the gender recognition bill that the UK parliament later vetoed,
he said:
"Trans women are among the most vilified, disenfranchised, and stigmatized people on this planet,” Madrigal-Borloz said. “Through my work in dozens of countries I have witnessed shocking acts of violence to which they are subjected, including killings, torture, beatings, and systematic social exclusion from health, employment, housing, and education.
"United Nations human rights bodies that have spoken on the matter have constantly found that legal recognition of gender identity through self-identification is the most efficient and appropriate way to ensure the enjoyment of human rights, and I am yet to learn of a country in which this is not the case.”
“Throughout history, unsubstantiated myths falsely portraying marginalised groups of people as dangerous to others have been levelled to try to justify imposing arbitrary and deeply discriminatory restrictions on their human rights,” said Madrigal-Borloz.
“As recently as a few decades ago in the UK, and still today in many other countries around the world, such harmful myths falsely portrayed lesbian women and gay men as predatory – causing great harm. Today, we see such harmful narratives repackaged and redeployed against trans women.
“The only connection between obstacles to legal recognition for trans women and freedom of all women from gender and sexual-based violence is based on erroneous views of trans women as being predatory or, equally shockingly, as not existing at all,” he said.