You can legally advertise a role as being open to applicants of one sex only if there is a 'genuine occupational requirement' to do so. Many jobs are legally advertised as being for men or women only.
Rape crisis centres do not 'get away' with anything! They closely follow the law.
The Government's guidance on this is here (with links to the Equality Act):
www.bis.gov.uk/policies/higher-education/access-to-professions/prg/legal-issues/genuine-occupational-requirements
For those who don't want to read the links, the Government says:
'It may be lawful for you as an employer to treat people differently when recruiting. In very limited circumstances, if you can show that someone with a particular protected characteristic (on grounds of age, disability, gender reassignment, marriage and civil partnership, race, religion/belief, sex or sexual orientation) is central to a particular job, then you can insist that only someone who has that particular protected characteristic is suitable for the job. This would be a genuine ?occupational requirement? (GOR). There is no definitive list of situations where a GOR will exist. It is therefore always best to take legal advice before advertising the job if you believe that there is a GOR.'
It says, with regard to sex discrimination exemption:
'The Equality Act 2010, Part 1, Schedule 9 provides that direct discrimination on the basis of sex is not unlawful where there is a GOR. A GOR may exist for various reasons:
if "the essential nature of the job would be materially different" if carried out by someone not of the required sex (eg an actor playing the role of the opposite sex)
where it is necessary to preserve decency or privacy (eg a shop assistant providing a bra-fitting service or a prison officer carrying out body searches)
if the employee is required to live in accommodation that is not equipped for people of that sex and it is not reasonable for the employer to make the necessary adjustments
if the job can most effectively be performed by a person of a particular sex'