Some examples:
In 1996: Vocally opposed the appointment of a trans woman (a physicist) to her college institution (Newnham College for Women), resulting in the physicist's outing to the UK tabloids (a source of immense distress for her over the following years). Greer resigned in protest when her opposition amounted to nothing.
In 1999: Published a book called "The Whole Woman" with a chapter on trans women called "Pantomime Dames":
"Governments that consist of very few women have hurried to recognise as women men who believe that they are women and have had themselves castrated to prove it, because they see women not as another sex but as a non-sex. No so-called sex-change has ever begged for a uterus-and-ovaries transplant; if uterus-and-ovaries transplants were made mandatory for wannabe women they would disappear overnight. The insistence that man-made women be accepted as women is the institutional expression of the mistaken conviction that women are defective males. The biological truth is the opposite; all biologists know that males are defective females. Though external genitalia are the expression of the chromosomal defect, their removal will not alter the chromosomal fact, any more than removal of the tails of puppies will produce a tailless breed. "Sex-change operations" can only be carried out in Swift's Laputa."
"The transsexual is identified as such solely on his/her own script, which can be as learned as any sex-typed behaviour and as editorialized as autobiographies usually are. The lack of insight that MTF transsexuals usually show about the extent of their acceptance as females should be an indication that their behaviour is less rational than it seems. There is a witness to the transsexual's script, a witness who is never consulted. She is the person who built the transsexual's body of her own flesh and brought it up as her son or daughter, the transsexual's worst enemy, his/her mother. Whatever else it is gender reassignment is an exorcism of the mother. When a man decides to spend his life impersonating his mother (like Norman Bates in Psycho) it is as if he murders her and gets away with it, proving at a stroke that there was nothing to her. His intentions are no more honourable than any female impersonator's; his achievement is to gag all those who would call his bluff. When he forces his way into the few private spaces women may enjoy and shouts down their objections, and bombards the women who will not accept him with threats and hate mail, he does as rapists have always done."
In 2009: Wrote an article for the Guardian on Caster Semenya, including a diatribe on trans women:
"Nowadays we are all likely to meet people who think they are women, have women's names, and feminine clothes and lots of eyeshadow, who seem to us to be some kind of ghastly parody, though it isn't polite to say so. We pretend that all the people passing for female really are. Other delusions may be challenged, but not a man's delusion that he is female."
In 2015: On a BBC programme, just within the last day:
“Just because you lop off your dick and then wear a dress doesn't make you a fucking woman. I’ve asked my doctor to give me long ears and liver spots and I’m going to wear a brown coat but that won’t turn me into a fucking cocker spaniel. I do understand that some people are born intersex and they deserve support in coming to terms with their gender but it’s not the same thing. A man who gets his dick chopped off is actually inflicting an extraordinary act of violence on himself.”