It's quite interesting if you read the original job description (linked earlier in this thread). The first part reads-
'Established in 1978, Edinburgh Rape Crisis Centre (ERCC) provides a specialist support, information and advocacy service for women, non-binary people, members of the trans community and young people aged 12 and over in Edinburgh, East and Midlothian who have experienced recent or historic sexual violence, including rape, sexual assault, childhood sexual abuse and commercial sexual exploitation. We also work in schools and with young people across Edinburgh and the Lothians, and strategically with multi-agency partners, towards preventing sexual violence.'
And if they 'provide women, non-binary people, members of the trans community and young people aged 12 and over', then it seems reasonable that a trans person might be considered for the post.
However, later in the job description it is stated that only women may apply, citing Schedule 9, Part 1, Paragraph 1 of the Equality Act 2010 , which is based on a protected characteristic (in this case sex) which means that the person who was the successful candidate in this case does not meet the criteria.