Defending her in a column, written on March 2, Ms Moore said: 'We have gone through the looking-glass and are being told that sex is a construct.
'It is said that sex is merely assigned at birth, rather than being a material fact – actually, though, sex is recognisable in the womb (which is what enables foetal sex selection).
'Sex is not a feeling. Female is a biological classification that applies to all living species. If you produce large immobile gametes, you are female.
'Even if you are a frog. This is not complicated, nor is there a spectrum, although there are small numbers of intersex people who should absolutely be supported.'
She adds: 'The materiality of having a female body may mean rape or it may mean childbirth – but we still seek liberation from gender.
'In some transgender ideology, we are told the opposite: gender is material and therefore can be possessed by whoever claims it, and it is sex as a category that is a social construction. Thus, sex-based rights, protected in law, can be done away with.
'I know from personal experience the consequences of being deemed transphobic by an invisible committee on social media. It has meant death and rape threats for me and my children, and police involvement. I also know that the most vicious stuff takes place online and not in real life. Still, I can't stand by.
'Most people want the tiny percentage of the population who are trans to have the best lives they can.
'Male violence is an issue for women, which is why we want single-sex spaces.'
In an article for The Spectator on March 14, Ms Moore wrote: 'A glance at Twitter after my Guardian column went online suggested that either I was the saviour of all 'natal women' or had committed some kind of transphobic hate crime.
'My offence was to say that biological sex is a thing. Scientists tend to think it is.
'After all the online abuse, I thought someone might ring me and see if I was OK, but they didn't. But then I never go to the Guardian office. There had been melodrama, apparently.
'A trans woman who had seemingly resigned some weeks earlier resigned again. My words had made her feel unsafe, she said. More than 300 employees at the paper signed a letter condemning the decision to run my article.
'I like freaks. I like fluidity. I just don't like one set of rules being replaced by another.
'I was hurt that so many of my 'colleagues' denounced me, but I suppose everyone needs a hobby.'
A Guardian News and Media spokesperson said: 'We wish Suzanne all the best with her future career and are sorry to see her leave.'
Meanwhile, Professor Todd has today praised Ms Moore in a tweet, saying: 'Thank you to Suzanne Moore for standing up for me (despite fact we disagree on many things), letting me know that my story mattered, that what happens to women is news, worth understanding, analysing, representing.
'The Guardian just lost a brave female voice.'