I saw an interesting comment from a poster on Quora recently where he or she said that, since MPs and ministers in the UK and the Commonwealth realms must swear an oath of allegiance to the Queen, they cannot support a republic without being in breach of their own oaths. I don't see it that way though.
As far as I understand, the oath of allegiance today is not meant to be a statement of personal allegiance to the Sovereign, but rather an acknowledgment that you recognize the legitimacy of and submit to the authority that proceeds from the Sovereign (or "the Crown") under the constitution.
In that sense, an MP or a minister would be clearly in breach of their oaths of allegiance if, as the Americans in 1776, they engaged in an insurrection which would attempt to overthrow the Queen's government and the Queen's laws unilaterally by violent and extra-legal means. However, if they pursued a transition from a monarchy to a republic by legal means under the established constitutional order, they would still remain "loyal" as the legislative power under the Crown also includes the possibility of the Queen or the Governor General in a realm disbanding their own offices by assenting to legislation (or, in the case of Canada, issuing a constitutional amendment proclamation) to that end once the necessary conditions laid out in the constitution have been fulfilled.
Why do you think? Does it make sense, or is it a stretch, and the Quora poster is actually right?