There are a range of opinions on that question! in the years I was growing up a great deal of science fiction was in the dystopian field (a lot still is!), and it certainly influenced some of us. Like the 'western' genre it often promoted the lone hero who triumphs through determination, ability and courage. It certainly has a huge influence on those who still follow that idealised view. There is certainly some evidence to suggest that certain types of story do colour our view of the world, though perhaps not quite as heavily as Sir Terry Pratchett's concept in his book "Witches Abroad." Certainly the so called fairy tales we are told as children shape our view of the world to some extent, probably as they were meant to. The stories of the Brother's Grimm, Hans Christian Andersen, Lewis Carroll and others all have moralistic and cautionary aspects, and that is true of other tales as we expand our literary horizons. Writers like Enid Blyton left many of us with a certain 'vision' of Britain, as did some of our less cerebral reading matter, like the Beano, the Lion, the Tiger and later more weighty weeklies like Look and Learn. Some of us will remember the more anarchic magazines like Mad ... They all played a part in framing some of our early views of the world, and how it functioned.
As I wrote in an earlier post, writers like Asimov, Heinlein, Clark and other scifi giants toyed with ideas for a future world, sometimes a rather dark and dystopian vision. It struck me recently that in several of those authors' portfolios there were some visions of future political developments which could be seen as being predicative of our present. In those stories the course of history is altered by the triumph of ideologies or 'players' the founders of the particular society in the story had failed to anticipate, or had anticipated, but believed could be constrained. Certainly the course of our societies is currently apparently taking a path I suspect very few would have predicted ten or fifteen years ago -- or, if they did, kept it quiet. It is certainly true that any writer wishing to create a fictional world or society has to look at the political philosophy prevailing and try to see where it might lead, what could change it, or possibly overthrow it.
Which brings me back to the question in the title. How much do 'stories' shape our outlook? In one sense it appears to be quite a large influence on us, but it depends on our choice of reading matter. A person who reads exclusively horror genre is not necessarily going to turn into a monster, nor will someone who reads extensively in the crime genre become either a career criminal or a policeman. It is much more subtle than that. The essence of the impact is in the subtle background of the story -- as one writer put it, it's the texture of the wall the painting hangs upon that enhances the idea it conveys. Consider Dickens as an example. Many of his stories are rather bleak, but they all contain an element of hope and of courage in difficulty. Dickens managed to convey a sense of injustice, and a desire to see justice done without hitting his reader between the eyes with it. He let the circumstances and the characters convey it all through their actions. This is also true to the original versions of the fairy tales we heard as children (and the element Pratchett plays with so masterfully in his discworld fantasies). Many, in their original versions, were seriously looking at major political and societal issues of their time, some, if not all, of that has been lost in the 20th Century 'sanitising' the Grimm's tales (and the rest) have undergone.
The bottom line really is that any writer must inevitably paint a backdrop of the sort of society his story is set in. If the writing has an historic setting, one has to be careful not to introduce 'modern' ideas or philosophies, whereas in a 'future world' scenario one has the liberty to explore alternative concepts or to extrapolate current political or ideological ideas to see where they lead. Orwell's 1984 fits that category -- and there is a book that has certainly focused some minds on a really dreadful possible society!
Ideas have power, but unless they are put into words, they remain 'just an idea'. Once given expression in a story, those ideas can become an inspiration, a force to be reckoned with if you like. Writers like Orwell were aware of that, and used it to good effect. I would certainly not put myself in anything like the company of authors like him, Tolkein, Dickens, Asimov or King, but I would hope that at least my worlds in my books at least appear plausible, perhaps recognisable. If perchance they also make one think about our real world I would be delighted.