In such cases, the courts would be tasked with determining if the organization’s policy was a proportionate means of achieving a legitimate aim or if it breached the Act as interpreted by the Supreme Court.
No. Stop making up your own legal procedures and tests. There is no “proportionate means to a legitimate aim” test that would make what you’re suggesting lawful. You’ve copied a bit legal jargon that’s floated around on the internet and applied entirely wrongly. A lot of people make the same mistake, but it’s still a mistake.
A “proportionate means to achieve a legitimate aim” test is applied before a single-sex service can be offered. Safety dignity and propriety for women and girls is a prima-facie legitimate aim when it comes to being undressed and keeping men out is a proportionate means to achieve that. Once that test is met there is no further “proportionality test” to opt in or out on a case-by-case basis.
Secondly, Charity law doesn’t have any such concept as proportionality. Charities must be operated for the benefit of their stated beneficiaries: in the case of GG, that’s girls. There’s no “but we can include others as long as it’s for a good cause”. It’s unlawful to do so, full stop. (Or, “period”, if you prefer.)