In the UK there exists a republican movement (i.e., those advocating for the replacement of the monarchy), chiefly focussed around a group called Republic.
Technically, advocating the establishment of a republic—even through peaceful means—is still illegal in the UK (though currently not enforced due to incompatibilities with the Human Rights Act 1998). However, the HRA appears to be firmly in the sights of the current government, so that might not be the case forever (though I imagine ‘bring back treason’ might be a hard sell, politically).
However, MPs who refuse to make an oath/affirmation of allegiance are treated ‘as if they were dead’ if they try to vote or join a debate, so it is clear that republicanism can still cause headaches in modern Britain.*
On the other hand, the Equality Act 2010 defines ‘philosophical belief’ as a protected characteristic that cannot be discriminated against, though with some exemptions. Republicanism appears to fulfil the criteria for such a belief.
Given this somewhat ambiguous legal environment, my question is: is it legal to discriminate against someone in the UK for peaceful republican advocacy, such as paid membership in a group like Republic?
And then some sub-questions:
Given that an oath/affirmation of allegiance is required for membership of the Armed Forces,† Parliament, etc., can these organisations deny or revoke membership for republican advocacy (provided they still make the oath/affirmation and don't breach other rules, such as claiming to represent the Armed Forces at political events)?
If the answer to #1 is ‘yes’, is this different for the reserve forces?‡
Can such advocacy be grounds for refusing meetings with royals?§
† The Armed Forces are explicitly exempt from four of the protected characteristics of the Equality Act, though not belief. As an answer to a previous question of mine explained, however, conscientious objection is nonetheless grounds for refusal or dismissal, so that appears to be a de facto exemption.
‡ Section 7 of the Reserve Land Forces regulations 2016 (for example) explicitly states that ‘Officers and soldiers of the Army Reserve...have the normal rights and responsibilities of citizens of the United Kingdom’, as opposed to Regular Army personnel.
§ Part of the reason I'm asking this question is also how I first heard of Republic - someone told me they had purchased membership for a monarchist friend as a joke, and that as a result they would never be allowed to meet a royal. However, I've not been able to find any evidence that this would be the case.