As a Canadian and British citizen (left-leaning), I am sentimentally and aesthetically a royalist, as long as the royals conduct themselves in a way that is aesthetically and ethically positive (and not too much public money is spent on them).
A monarch with a historic pedigree can, like a flag or soil, be a more palpable symbol for a populace to identify with, and take heart in (especially in hard times) than an appointed or elected figurehead. (My native Hungary's current presidential fiasco is a case in point.)
If the British royals ever did anything like that today, I would immediately become a republican.
(I'm rather afraid that if I took a closer look at current royals' domestic hunting, I might already become as anti-sovereignist, with reason, as the separatists [ironically calling themselves "sovereignists"] among my fellow-quebeckers already are, without reason, alongside Canadian and Australian republicans, likewise without reason.)