In first edition Mage, vampires fell entirely under the sphere of Matter, and changing the shape of matter was available at fairly low levels. (This was referenced in Book of Shadows, the Player's Guide to Mage, in a subhead: "Turning Vampires into Lawn Chairs and Other Works of 'High' Magick" -- although it wasn't a rote.) The notion that a starting mage could, with a wave of his hand/wand/athame, completely destroy a vampire — who, at the time, had no way to defend against it – was variously seen as a sign of how Mage was a broken system or that Vampire players were whiny gits.
As for how the meme got started, as with many things in the 1990s, it started on Usenet. In 1994, in a thread on alt.games.whitewolf, ironically, about how Wraith wasn't a sales hit (compared to games like Vampire), a poster named Jack Dracula wrote, in defense of Mage:
But this is also one of the best features. No D&D spell lists, this
inspires creativity and role-playing, rewarding creative gamers for
their quick thinking. What that does unfortunately do is attract
powergamers who want to turn vampires into lawn furniture, but they
are just as quickly turned away by either ST Balance ("The Nephandi
turned -me- into a lawn chair?!") or the lack of Power-Gamer Reward
(No new level to get, no dragon hoard to plunder, no next level of
In Second Edition and beyond, this was changed so that Vampires required both Life and Matter, but the notion of mages dispensing with vampires easily by transforming them into patio furniture persisted thereafter. (Werewolves always required Life, and in later editions Spirit, so I don't know what the players were thinking in that regard. Still, as part of the question, it gets an answer.)
How did it spread so fast? At the time, a lot of the people who wrote and worked for White Wolf hung out with posters on a.g.ww and on various online game sites like the Storyteller Circle MUSH. Jack Dracula was a frequent inhabitant of both places, and it gained currency just like the "whiskey flask" problem with Paradox. It was an inside joke that grew, and that's why people still reference it two decades later.