This claim is untrue and irrelevant. Even VisitBritain, our national tourist agency, can't find any evidence for it.
Chester Zoo, Stonehenge and the Roman Baths are all more successful tourist attractions than Windsor Castle, which is the only occupied royal residence to attract visitors in large numbers. If Windsor Castle was included in the Association of Leading Visitor Attractions (ALVA) list of top attractions it would come in at number 24.
Research shows that tourists come here for our world class museums, beautiful scenery, fantastic shopping and captivating history - not because they might catch a glimpse of Prince Andrew. In a republic, royal properties such as Buckingham Palace would be open all year round, so visitors that do want to explore our royal heritage would have even more opportunity to do so.
But, even if the claim were true, do we really want the whims of visiting tourists to determine what kind of political system we have?
Royal residence admission numbers can be found in the Royal Collection Trust's annual reports