I completely concur with PPs that this is not just about safeguarding, it is also about the right to privacy, dignity and the importance of girl only space.
However, regarding safeguarding, Girl Guides have very strict protocols on place of a male child of a guide leader wants to join them in a residential. If this child identifies as a girl, the protocols are abandoned.
Girl Guiding say:
“[W]e do allow volunteers’ family members to attend residential events. Such requests are carefully considered by the local commissioner and as a part of the mandatory risk assessment or any trips. However this same process would not apply to a trans girl as this would be a breach of the Equality Act.”
However, the Equality and Human Roghts Commission (the body charged with upholding the Equality Act 2010) disagrees. They say:
The exclusion of trans people from membership of organisations and access to benefits and services that they provide would normally constitute unlawful gender reassignment discrimination, unless this is expressly permitted and justifiable by reference to exceptions from the non-discrimination principle. The most relevant here being membership of associations (schedule 16 EA 2010) and the provision of communal accommodation (schedule 23 EA 2010).
As a single-characteristic association for the purposes of schedule 16 of the EA 2010, Girl Guiding UK can choose to refuse membership to trans girls, or choose to admit trans girls as members.
As a provider of communal accommodation for the purposes of schedule 23, paragraph 3, Girl Guiding UK can also choose to exclude or include trans girls. Operating trans inclusive policies is permissible, provided that this is consistent with the rights of others and justifiable. The risk of sex discrimination against other members can be a relevant consideration in this context.
These matters must be approached carefully and sensitively, without prejudice, stereotypes or unwarranted assumptions. We consider that a case-by-case approach to the operation of any exception, including the question of whether reliance on any exception can be objectively justified, will be appropriate and necessary. Where organisations decide to adopt trans inclusive policies and practices, the needs of all members or service users have to be considered in any particular case.
The EA 2010 does not prohibit the use of risk assessments and other safeguarding procedures where warranted in individual cases.
So GG have either misunderstood the Equality Act (unlikely, as they would have had legal advice) or they have been misled about their duties under the EqA (by who? Would be interesting to see who has advised them) or they are wilfully misinterpreting it to suit their own agenda.