Female-only swimming and gym sessions across Glasgow are to be opened up to cross-dressing males, sparking claims that women and girls’ sport in the city could “disappear”.

Rules designed to be inclusive towards trans men and women are so broad they render sessions designed to be single sex meaningless, while there are fears women could be deterred from general sporting activities if they feel unsafe in changing rooms or other areas.

As in many local authorities across Scotland, policies in Glasgow have been changing to be more inclusive of trans people, and staff have been told that anyone who identifies as male or female can take part in single sex sessions, or use the changing rooms they feel most comfortable with.

However, the definition used by Glasgow Life, the council’s arm’s length sport and leisure body, not only includes people who have fully transitioned, or are living as an adopted gender, but anyone who identifies as trans, including men who simply cross-dress.

“The person is entitled to participate in single sex sessions and cannot be excluded from participation of (sic) their chosen gender,” the guidance to staff says.

It provides a range of definitions of those who may participate in such sessions, including people who have transitioned or are transitioning from one gender to another and people who were born “intersex” and people who reject gender definitions.

It adds that the policy includes: “Cross-dressing people (who cross dress because they feel more comfortable expressing themselves in masculine or feminine clothing).”

The guidelines say any customers who object, should have the policy “sensitively” explained to them.

Read more: Vic Valentine: Recognise people by the gender they live

“Some customers may complain if they feel that someone whom they think of being of the opposite sex is in their changing room. This is understandable and it requires sensitive explanation of .... our policy of trying to facilitate equal access within our venues.”

But such customers may be unlikely to get a sympathetic hearing, as in the same section staff are urged to “use the Hate Crime Reporting Form for any incidents”.

Some women campaigners argue this fails to consider the needs or rights of other service users, and claim single-sex activities or changing rooms cease to be a meaningful concept if anyone can access them.

Susan Sinclair, who tweets and blogs as Scottish_Women, said it was astonishing the policy had ever been agreed, and that, by law, an assessment should have been done about how it might affect other people using the facilities.

“Glasgow Life’s ‘Guidance on Accessing Sports Facilities and Service by Transgender People’ is yet another example of a policy change by our Public Authorities that misinterprets the 2010 Equality Act,” she said.

“There would appear to have been no public consultation or Equality Impact Assessment carried out for this change of practice.

“Single sex changing rooms and showers are permitted under our Equality law, and this would include the exclusion of trans people of the opposite sex.

“Yet Glasgow Life wrongly state that the Equality Act 2010 allows trans people to choose their changing and showering facilities.

“This is extremely alarming and is wide open to abuse from sexual predators.

“Glasgow Life needs to urgently review their guidance with a view on how this negatively impacts on women and girls who have sex based protections.”

Read more: Susan Sinclair: Female rights must be respected

Writing in the Herald today, Vic Valentine – policy officer with Scottish Trans – says: “The definition used of who has the protected characteristic of gender reassignment does not require them to have undergone any medical treatments, or to be under medical supervision... The law and its protections are broad, and rightly cover trans people in the early stages of living in their gender identity.”

The row comes after revelations of internal discussions with the SNP over the concerns of a number of MSPs at the party’s stance on gender recognition and gender self-ID.

Critics argue policies such as Glasgow Life’s could particularly discourage children, people with a history of trauma or abuse, or people who cannot share changing facilities with someone they believe to be the opposite sex for reasons of culture or faith, preventing them from taking part in sporting activities. However the leisure organisation said its aim was to remove barriers to participation.

A spokesman for Glasgow Life, said: “Equality is at the very core of everything we do.

“We work to break down any barriers to access across our services and facilities, while ensuring that everyone can take part while feeling safe and secure.

“Our policies reflect that and are designed in response to national guidance and legislation.

“If anyone, at any time, feels uncomfortable in using our services, they should immediately contact a member of staff.”