The royal family memorabilia isn't such a big thing anymore (very few younger people want a collection of tea towels and mugs with royals faces on them sitting in a drawer), and even when it was it didn't bring in anywhere near enough money to justify their existence. The stuff that sells the best is still Diana memorabilia, so it's nothing to do with being a living/active royal anyway.
They bring in some (pretty weird) tourists when they get married or hit a big milestone, but we're talking the same amount who might travel here to see an exclusive concert or show. It's something, but it's really, really minimal.
Some tourists come primarily for the historic royals and related sightseeing, but getting rid of the current monarchy doesn't mean everyone will suddenly lose interest in Elizabeth I and Richard III and so on. If anything it would increase tourism, as more historic buildings could be opened to the public.