Yes there are exceptions. This does mean that not every story set in the future is science-fiction.
The novels Stella Gibbons' Cold Comfort Farm (1932) and Evelyn Waugh's The Loved One (1948) are set in the future. Certainly, in the future of the time when they were written and published. The futurity of these works isn't obvious, it appears as hints in the text and is due to the intent of their authors.
Decades ago I discovered a play in book form written by, I believe, Arthur Koestler. Subsequent searches, for example on Wikipedia, failed to unearth any information about its existence. Probably, published in the late nineteen-fifties. This was held by a university library and they have extensive collections of published material.
This play had an introduction that said that it was set in the future, but that it wasn't a work of science-fiction.
The technothrillers of Dale Brown and Tom Clancy may qualify as fiction set in what can be considered as the near-future where the advanced technological devices and systems depicted in them have been developed and are in service. However, that is likely to encounter the hair-splitting about genre divisions and categories. Technothrillers can be considered both of and not part of science-fiction depending on how a given person views those genres.
Interesting category distinctions also exist around Peter Dickinson's The Blue Hawk (1976). This book is set in an imaginary desert kingdom rued by an ancient priesthood. It appears to be a fantasy version of Ancient Egypt. However, the author himself has explicitly stated that it's set in the far future. Because there are creatures present in the story that are alien species imported from the stars. Presumably, there was a future era (from our point of historical view) when interstellar travel was possible, but this lies in the past of the story's world and has been long forgotten.
This is the case of a book apparently set in an imagined past, that is to all intents and purposes fantasy, but the fictional apparatus to bring into being are science-fictional.
Again there are all the awkward genre categorizations about whether works of fantasies where the underlying worldbuilding is science-fictional are forms of fantasy or should they be regarded as science-fiction. The possibility of them being both cannot be ruled out.
In conclusion, there are stories set in the future that are not science-fiction. Some are certainly close cousins, if not more intimate relationships. This author is sure there are more stories set in the future, most likely the near-future, that may appear to be set in the present era of when they were written and published. Finding them can be a challenge.