I wouldn't go around and label myself an anti-monarchist but I'm surprised that that's a contentious position? Yes, of course the people should strip all power from their monarchies/monarchs/aristocrats in a democracy, because democracy is about sovereign power originating from the people or whatever, not from divine right or right of conquest or tradition or something. And yes, of course historic monarchies are at least equally objectionable! As a rule I'm pretty sure they exploited people a lot worse than at least the present-day monarchies we tolerate for whatever reason!
If the monarch as a person has present widespread support from the population they can probably do the aristocratic equivalent of a gofundme to keep living in their pretty palace if that's what the population wants, and then get elected to normal political offices like a normal person. If the monarch as an office has present widespread support I'm going to quietly disagree with the population and in the case of the UK at least roll my eyes a little.
As has been noted, strange women lying in ponds distributing swords is no basis for a system of government.
Curious why? Would you hold that position even if the monarch has present widespread support from the population?
Do you think something has changed to make that form of rule more objectionable than it was in the past? I.e., do you have an equally negative view of historic monarchies?