If we must choose between ceremony and democracy the choice must be democracy. Few tourists ever see the Queen or any member of her family. When they have gone the tourists will still be able to watch the Changing of the Guard and other ceremonies. And they will also be able to tour Buckingham Palace and view the royal treasures. That will mean more foreign income for Britain.
Republicanism has nothing to do with left or right wing politics.
Republicanism allows for differing opinions about economic policy and the role of the state in society. In Ireland republicanism has been entwined with the movement for national independence and such movements often resort to violence. However, most Irish republicans have for long been committed to non-violent methods. Look at the massive social problems in the United States. Both Britain and the USA have social problems.