It comes as Harry Potter author JK Rowling, who has previously tweeted a picture of herself wearing a T-shirt calling Nicola Sturgeon a “destroyer of women’s rights”, described Ms Regan on social media as a “heroine” for the stance taken.
MSPs endorsed plans to make it easier for someone to change their legally-recognised gender by 88 votes to 33 last week, with four abstentions. In total, nine SNP MSPs defied the whip with seven, including Ms Regan, voting against the plans and two abstaining.
Ms Regan said: "My beliefs and my commitment to building a better Scotland for all of us, but especially for women and girls, is what drives me as a politician. It drives my politics, it drives me as a person as well. I think last week for the SNP, the vote should have been a free vote.
"I think that healthy debate is important. I think that robust challenge is, after all, how we create good law and I think that actually is a strength and it’s not a weakness.”
She added: “My conscience would not allow me to vote for a Bill where I could not be 100 per cent certain that women and girls would not be in danger. I am not against reforms that make the lives of trans people better, but I want us to get into a place where we can respect everybody’s rights.”
In a frosty response to her resignation letter, Ms Sturgeon said at “no stage” had the former minister approached her to “raise your concerns” about the Bill.
The SNP leader said: “I note that at no stage have you approached me – or indeed the Cabinet secretary for social Justice – to raise your concerns about the Gender Recognition Reform Bill or the vote this evening.
"However, in circumstances in which a minister is unable to support the Government, it is the case that the only options available are resignation ahead of the vote or dismissal thereafter. I therefore accept your resignation."
Asked what she made of the First Minister’s reaction to her resignation, Ms Regan said: “The First Minister was well aware of the concerns that I held on this issue.”
However, Government sources said it was obvious Ms Sturgeon had been aware of the issues and the letter referred to the lack of a direct, one-to-one meeting on the issue with the First Minister or Permanent Secretary outlining her opposition.
A Scottish Government spokesperson said: “A minister who considers they cannot comply with collective responsibility should approach the First Minister to discuss the issue. Ms Regan was free to do so – at any stage from her accepting appointment as a minister, in full knowledge of Scottish Government policy on this issue, up until the parliamentary vote last week – but chose not to.
“Ms Regan’s concerns were well known, publicly and privately, and the First Minister’s letter does not say she was unaware of Ms Regan’s views. Rather, the letter makes clear that at no point did Ms Regan make use of the well-established practice by which any minister can approach the First Minister when they have a difficulty. Nor did she make use of the specific facility to meet with the Cabinet secretary for social justice on this issue, as other MSPs have done.”
Tory equalities spokesperson Rachael Hamilton said Ms Regan should be “applauded for staying true to her principles” and resigning.
She said: “Ash Regan has made it abundantly clear that she believes she made Nicola Sturgeon fully aware of her concerns over this Bill, in complete contrast to the First Minister’s version of events. The onus is on Nicola Sturgeon and the SNP to ensure that valid concerns from their own MSPs are listened to as the Bill progresses.
“Currently, Ash Regan and her fellow SNP rebels feel – as women’s groups do – that their concerns are being dismissed, which left them with no option, but to defy their party last week. The Scottish Conservatives will allow our MSPs a free vote at every stage and Nicola Sturgeon should do likewise.”