Only a few on this list are genuine villains as opposed to mere antagonists.
Gaston in Beauty and the Beast, and Frank in Rocky Horror are two of my favorite examples of a pure sociopath in the musical theatre canon. Gaston's brainless appearance as an egotist conceals the fact that there is literally nothing he would not do to get what he wants, regardless of who he needs to hurt. In fact, in "Gaston Reprise" and "Maison Des Lunes," he is shown to take pleasure in hurting people as collateral damage.
Doctor Frank-N-Furter is often misread as the hero of Rocky Horror, a pillar of sexual liberation and queer pride. This, not coincidentally, is how he clearly sees himself. But his castle full of fawning followers is actually a clue to his darker side- over the course of the Rocky Horror Show (and more so in the movie), we see that he is a master manipulator, a rapist, a murderer and a hypnotist strong enough to hold everyone else in the castle in his thrall. When he sings "give yourself over to absolute pleasure," as every character in the movie, now dressed more or less like him, dance around in hypnotic trance, it's not the triumph of liberation but the triumph of the will- Frank's will.
I agree with the folks that say there is a difference between an antagonist and a true villain. In fact, I can think of lots of musicals without a villain (e.g, My Fair Lady, The King and I, The Producers, La Cage aux Folles) but, without some kind of antagonist, there is never a successful story, whether that story is a mystery, romance, or sci fi novel, a comedic play, or a musical.
I'm on the fence as to whether Javert is a strong antagonist or a villain, although I lean towards villain. I also wonder how to classify villainous protagonists, such as Henry Hyde, Sweeney Todd, or my personal favorite, the Phantom. Are they villains or are they misguided? Maybe, they're a bit of both.
Miss Hannigan - Annie Mrs. Meers - Thoroughly Modern Millie Gaston - Beauty and the Beast Any number of the characters in Matilda Jigger - Carousel Kodaly - She Loves Me The Snake - The Apple Tree and... The War - Ms. Saigon Prejudice - South Pacific
I think most of us are using "villain" in a broad sense, as befitting musical theater antagonism. With the notable exception of Simon of Legree as performed by the Court of Siam, there are few absolute monsters in musical theater.