They are not conservatives anymore. Most of them support the Liberals or NDP nowadays.
This is a classic example of showing in Canada, some people are monarchists but does not mean they will be politically conservative.
In fact, a lot of members of the Monarchist League seems to me like "Down with American imperialism and support progressive social justice! Long live the Queen!" in beliefs i.e. a Chomskyite but believe the HOS should be a monarch.