The event, which will be addressed by leading UK feminists, will discuss the rights enshrined in the UN's Convention on the Elimination of all forms of Discrimination against Women, and ask whether they are at risk as laws move towards replacing sex with gender.
Women due to speak at the event, include writer Julie Bindel and Professor Rosa Freedman, an expert in law, conflict and global development from Reading University - both of whom have previously been accused by trans-rights activists of being "transphobic" because they believe that women's rights are not the same as trans rights.
But the Edinburgh University's Students' Association Liberation group said that in holding the discussion the university is "stirring up transphobia" and demanded "No TERFs on our turf". TERFs - trans exclusionary radical feminists - is a word regarded as a slur by many women campaigning for sex-based rights and last week in the House of Commons a representative from Twitter agreed with Joanna Cherry MP that it was the equivalent of "b****" and "c***".
In a string of tweets, which were approved by the main student organisation EUSA, the Liberation group said: "After a year of fighting transphobia on campus, we are disappointed and angry to see the University once again being made unwelcoming for trans people.
"Arguments under the guise of ‘sex-based rights’ all too frequently lend themselves to denying the rights of trans people to be recognised in their gender. We firmly support an intersectional feminism that includes all women, trans and cis, and oppose the University’s promotion of people widely criticized for stirring up transphobia.
"Discussions on women’s rights must include ALL women, including trans women, and move beyond outdated, exclusionary understandings of feminism. #NoTERFsonourTurf."
Despite the protests, the free event organised by the university's Institute for Education, Teaching and Leadership, no longer has any of its 200 tickets available.
And in a letter to a former graduate who wrote thanking the university for supporting the event, the principal Professor Peter Mathieson, said that universities should be "safe places for complex and sometimes controversial discussions to take place."
He added: "There will be many that disagree with views expressed at the event: the challenge to those people and indeed to the speakers is to accept that everyone has the right to be heard and that contrary views should be treated with respect. I hope and expect that the event will take place in that spirit."
Today Prof Freedman said: "Edinburgh University is one of the few universities in the UK where a staff member has still felt able to hold an event focused on women's sex based rights. Too many academics don't feel secure enough within their institutions to propose these events let alone to run them. It is really disheartening to know how many gender critical academics there are who feel unable to organise an event like this."
She added: "Peaceful protest is a legitimate part of a functioning democracy and I will fight for people's right to protest as much as for people's right to free speech. By enabling the event to go ahead and not allowing it to be shut down, Edinburgh University is doing the right thing here."
Another speaker, former Scottish Government policy analyst, Lucy Hunter-Blackburn added: “Universities should be leading the way on enabling respectful discussion of different perspectives here. With this event and a transgender conference at the end of May, Edinburgh is rightly doing just that.”
The event publicity says the discussion will be around a declaration made in March by the international feminist group ‘Object!’, that women's rights, "as enshrined in the 1979 UN Convention on the Elimination of all forms of Discrimination against Women (CEDAW), are at risk and need to be reaffirmed."
It continues: "The writers of the declaration say that, “Recent changes replacing references to the category of sex, which is biological, with the language of ‘gender’, which refers to stereotyped sex roles, in United Nations documents, strategies, and actions, has led to confusion which ultimately risks undermining the protection of women’s human rights.
"The confusion between sex and ‘gender’ has contributed to the increasing acceptability of the idea of innate ‘gender identities’… ultimately leading to the erosion of the gains made by women over decades.”
"With sexism and misogyny still sadly much in evidence, are the writers of the Declaration justified in their belief that women’s sex-based rights are potentially being undermined? What protections are still needed? And what can, and should, be done to reassert and protect those rights, globally and here in Scotland?
"This multi-disciplinary panel will consider future ways forward for women’s rights in a world of complex sex and gender relations. There will be plenty of time for open discussion and all viewpoints are welcome, though we remind all participants that dialogue should be measured and respectful in tone."
As well as Julie Bindel, Prof Freedman and Ms Hunter-Blackman, other speakers include Dr Louise Moody a philosophy research associate at York University and Professor Sarah Pedersen an expert in communication and media at Robert Gordon University.
But EUSA Liberation was backed on Twitter by Edinburgh's radical bookstore Lighthouse Bookshop, which tweeted: "Amidst news that @EdinburghUni are hosting a gathering of misogynistic transphobes (more anon) let’s remember they are a vocal, hateful minority-we are many & our community is strong & vibrant & the bigots don’t get to dominate our narratives #WeAreEverywhere #transpride."
It added: "ACT: write in & call out @EdinburghUni & @MorayHouse for the hypocrisy & transmisogyny in platforming bigots like JulieBindel & RosaFreedman who use these opportunities to legitimise their hatefulness: their actions put lives at risk,encourage marginalisation &discrimination."
The bookshop goes on to promote a Transgender:International/Intersectional Conference which also takes place at Edinburgh University at the end of May which has been organised by Gina Maya Roberts, a PhD student of Global Transgender narratives.
An official statement from Edinburgh University said they had received a number of comments "both negative and supportive" about the event. It added: "The University of Edinburgh should be a safe place for difficult conversations. We are committed to defending freedom of speech and expression, as long as it is carried out within the law and in a respectful manner.
“Given the size of our community, it is inevitable that the ideas of different members will often and, quite naturally, conflict. We encourage members of our community to use their judgement and openly contest ideas that they oppose, and feel protected in doing so.
“The event in question was approved by the University Compliance Group, which considers any event that might compromise the University's duty towards equality and protecting freedom of expression."