Well first of all, I think there's a selection bias at work in our assessment of who "changed the world". The Royal Society looks world-changing now, but in its day it probably just looked like a bunch of eccentric tinkerers and nerds. It took centuries of progress, based on the foundations discovered in the 17th century, for those contributions to be properly recognized as world-shaking.
Second, I think whether groups are able to make big changes, especially in the social sciences, depends in large part on external events - i.e., whether there are big political changes happening at the time, for other reasons. The Meirokusha came along during a time when Japan was undergoing rapid opening and industrialization, and the Scottish Enlightenment came just before the Industrial Revolution, a wave of revolutions in Europe, and the formation of the U.S. and the British Empire. Right now, the world is in a relative period of stability (knock on wood) - it's hard to find recent groups that changed the world, because the political world just hasn't changed that much.
But given these caveats, I think it's still clear that a relatively small community of smart people can change the world.
One example would be the group of physicists, mathematicians, and engineers who came out of Europe in the early 20th century - Einstein, von Neumann, Bohr, Fermi, Schrodinger, and all the rest. These folks did a lot of groundbreaking physics and math, but they also invented refrigerators and nukes, made major advances in economics and computing, and probably did more to reinvent science than anyone since the Royal Society. The modern world is largely built around technologies and ideas that came out of that community. They weren't as cohesive of a group as the Royal Society, but they did mostly know each other, and there was probably significant cross-pollination of ideas.
Another group that changed the world was the Chicago School of economics. In the mid to late 20th century, the Chicago economics department saw a remarkable confluence of talent - Gary Becker, Robert Lucas, Milton Friedman, Ronald Coase, Frank Knight, and many others. The ideas that came out of that community changed the face of modern society. Some of those changes are things that many people don't like, but the same is true of the Scottish Enlightenment, the Meirokusha, the Progressives, the Fabian Socialists - indeed, the same is true of any social science community. The Chicago School thinkers were specialized in social science, but within that broad category, their ideas were remarkably general, dealing with almost every important social, political, and economic issue of the day.
Both of these communities could also reasonably be described as "rationalist". They were specialized, but not hyper-specialized - Einstein invented a refrigerator, Milton Friedman wrote political philosophy, etc. They had their ideological biases, at both the individual and the group level, but most of them were keen on figuring out how the world really worked (though there might have been exceptions to this).
Of course, just because it happened recently doesn't mean it could happen again. The 20th century might have seen the last great scientific advances that the human race will ever make. The ideas of the Chicago School might be the last coherent, original, influential outpouring of social thought. But note that this was just as possible in 1870, or in 1570, as it is today. There were probably scientists and social thinkers in those days who believed that everything important had been discovered and created. Almost by definition, big paradigm shifts in either natural or social science come unexpectedly.
A more worrying argument is that modern intellectual communities are too highly specialized. Some believe that science is just so hard now that progress can only be made by teams of super-specialized people digging deep into one domain. Others think that the incentive structures of modern academia, business, government, etc. encourages too much specialization.
I'm not sure whether science is too hard for generalist communities of polymaths to make big breakthroughs. The biggest scientific breakthroughs usually involve the establishment of completely new fields that few people were working on before - physics in the 1600s, electrical engineering in the 19th and early 20th centuries, computer science in the 20th century. We might have run out of new domains of knowledge, or we might not have - in fact, we'll never know whether we have or not.
I do worry about incentives. Modern academia is very siloed - there's a lot of pressure to publish in your own field's highly specialized journals. Scholars who venture into other areas, with new perspectives - think of Gary Becker trying to do sociology - are often resisted and even vilified as "imperialists" by the existing research community. Specialized academic communities can even become sort of like "mafias", resistant to new ideas.
I doubt that this is quite as big a barrier as many fear. The smartest people in their fields - think Terence Tao in math, Feng Zhang in biology, or Ivan Werning or Markus Brunnermeier in economics - have zero problem getting published in their own field, and have plenty of time to work on and think about other things. I picked these examples because they're all obviously highly curious people who have explored a lot of different fields within their discipline. Similarly, I don't think professional "mafias" will be able to successfully resist new ideas if those new ideas work. If Terence Tao went out tomorrow and made a macroeconomic theory that could predict the effects of monetary policy really well, I doubt even the most concerted resistance by macroeconomists could stop it from being accepted.
Meanwhile, the internet has opened up tons of opportunities for collaboration and cross-pollination. The economics blogosphere is a good example of this. In many ways, it's one of the most successful rationalist communities around today. Econ bloggers are often accomplished academics - Paul Krugman, Paul Romer, Narayana Kocherlakota, Brad DeLong, and others have all held faculty posts at top schools. But the range of topics the blogosphere deals with is fantastically wide - everything from presidential politics to art and culture to the history of science.
And though it's hard to tell, I'd say the blogosphere has had some real influence. The voluminous discussions of fiscal policy, as well as Krugman's forceful advocacy, have probably made austerity less popular across the developed world. Word of mouth tells me that relentless blogger criticism of macroeconomics has helped push younger academics toward more empirical and more micro-grounded research (and I think you can already see this in the literature). By publicizing the discoveries of academics' mistakes, such as with the Reinhart-Rogoff affair, econ blogs are also leading to a democratization of research evaluation and critique that might eventually challenge, or complement, the peer review system. And new ideas have come from the blogosphere - for example, Robin Hanson's use of signaling to explain social phenomena.
But the econ blogosphere has a problem - in order to have continued and expanded relevance, we need new people and we need more brain power. Much of the impetus for the efflorescence of blogging between 2009 and 2013 came from the Great Recession. The current crop of bloggers has had some spectacularly interesting exchanges - for example, Steve Williamson and Narayana Kocherlakota have a long-running monetary policy debate on Twitter that is more interesting than any other such debate I've ever seen. But for the blogosphere to become a rationalist community for the ages, we need more very smart people. We need polymathically inclined folks like Brunnermeier and Werning to start blogs, and to have exchanges of ideas on wide-ranging topics. If that were to happen, the blogosphere might eventually have an influence up there with the Chicago School. Currently, that is still a distant dream.