I can completely understand that line of thinking. One thing I would say is that the institution should not be assumed to be the same as the individual. One monarch who I have little time for is the Duke of Windsor (formerly Edward VIII); some of the things he has said are pretty vile and I do not really hold him in high esteem. However, our current Sovereign is a person who, although we share differing opinions on some things, I have complete respect for.
The institution of monarchy also brings people together, as well as dividing them (like in Ireland), and I would say that, whilst Ireland is a nasty part of British history, lots of us have moved on and tried to find a path that unites both the United Kingdom and Ireland, as well as the British Monarchy and Irish presidency.