Purists on both sides would no doubt strenuously disagree. Dune brims with futuristic technologies typically found in hardcore science fiction: energy shields, lasguns, starships, to name but a few. Lord of the Rings is packed with the fantastical elements of wizardry, plus mystical races and creatures.
So too does Dune. The sandworms of Arrakis revered by the Fremen - themselves akin to Elves in the broadest sense possible as a people deeply in tune with the land of their birth - are as overwhelming and enigmatic as dragons. The mysticism fostered by the manipulative Bene Gesserit witches rivals the sorcery enacted by the best and worst spellcasters in fiction. And young Paul Atreides, as the Kwisatz Haderach, is gifted with prescience, itself echoing the prophecies so often utilized in fantasy writing.
Still unconvinced that Dune can and should be equally regarded as fantasy? Take the Guild Navigators, humans evolved into distinctly new lifeforms through melange saturation. What are these beings, capable of guiding impossibly huge Heighliners across vast stellar distances using limited prescient vision alone, if not magical?
The late, great Arthur C. Clarke summed it up nicely in his Third Law: Any sufficiently advanced technology is indistinguishable from magic.
Dare I suggest that Herbert's epic be reclassified as Science Fantasy. Whatever genre you label it, Dune is a magnificent read and will endure as one of the all time greats of fiction.