Alright, let's look at what would have happened if they decided to 'break the law':
An individual who felt disadvantaged or excluded could initiate a claim under the Equality Act 2010.
This would focuson on whether the organization's policy constitutes unlawful direct or indirect discrimination.
The Charity Commission may also step in, which may result in adjusting policies to avoid the risk of regulatory action or "potential regulatory action from the Charity Commission" if their actions are deemed inconsistent with their charitable objects or legal obligations.
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.
The Supreme Court has clarified that organizations have the option to restrict membership based on biological sex, but they are not mandated to do so in all contexts.
What would happen is getting into way too much trouble for what it's worth, yet it would have still been possible to battle it all, as they were not directly forced to make this decision.
For any organization, the reputational risk, even if they technically won in court, also often acts as a bigger deterrent than the legal action itself.