https://www.equalityhumanrights.com/equality/equality-act-2010/your-rights-under-equality-act-2010/religion-or-belief-discrimination
'The Equality Act 2010 says you must not be discriminated against because:
- you are (or are not) of a particular religion
- you hold (or do not hold) a particular philosophical belief
- someone thinks you are of a particular religion or hold a particular belief (this is known as discrimination by perception)'
However, perhaps political parties are excluded on this basis:
'Circumstances when being treated differently due to religion or belief is lawful
...an organisation is taking positive action to encourage or develop a group of people with a religion or belief that is under-represented or disadvantaged in a role or activity
...
A difference in treatment may be lawful in situations outside the workplace such as if:
...
a religious or belief organisation is restricting its membership or participation in its activities, or the provision of goods, facilities and services to persons of a particular religion or belief. This only applies to organisations whose purpose is to practice, promote or teach a religion or belief, whose sole or main purpose is not commercial. A restriction can only be imposed:
if the purpose of the organisation is to provide services to one religion or belief
if it is necessary to avoid causing offence to persons with the same religion or belief as the organisation
an organisation is taking positive action to encourage or develop a group of people with a religion and belief that is under-represented or disadvantaged in an activity
the circumstances fall under one of the other exceptions to the Equality Act that allow organisations to provide different treatment or services based on religion or belief'
So, the SGP are effectively setting themselves up as an organisation promoting the particular belief that 'Transwomen (men) are women'?