They are an acquired taste alright. They appeal to musos more than to women. Their longevity certainly has raised them to cult status, also that Neil Peart, their drummer, withdrew from the band for hals a decade after he lost both his wife and his daughter. And they would not tour nor record without him. Their music is a mix of prog and hard rock, not quite either. The fact that three men make so much racket on stage without an army of backing musicians and tapes endears them to a lot of purists - any other band would have hired an extra keyboard player and a rhythm guitarist for tours long ago. Geddy's voice/squeal is love or hate, to many Rush fans it is more of the fourth instrument in the band than a transporter of emotion and lyrical content. Peart's lyrics are not Bob Dylan prose, but his attempts at tackling subjects above the heads of most rock bands appeals to their following to.
Rush are aware of their nerd factor status and play with it. They are proud men about their instrumental capabilities (rightfully so), but tongue in cheek about the fervor of their followers. The recent concert I saw featured intro and outro movies in-between vids where Geddy played a jewish barkeeper in Groucho Marx look, Peart was a stern army veteran or policeman (looking utterly convincing) and Lfeson played a greasy, mulleted manager in a fat suit of a hopeless - Rush lookalike -rock band. They certainly took the piss of themselves in those films, but at the same time they are devoutly dedicated to their musical craft.
Actually, the weirdest thing about Rush's sound - Geddy's vocals aside - is Alex lifeson's multi-layered and -delayed guitar playing which defies for most parts a blues and rock heritage. Lee and Peart are both busy and excellent players, but what they do in all its complexity is conventional playing, just very sophisticated.