In the old days, musicals tended to be highly idealistic comedies. This tendency has been largely lost in contemporary musical theatre: though idealistic shows (e.g. La Cage aux folles, The Producers) still are produced, about as common are cynical shows including snide Take Thats against idealism (e.g. Chess, Urinetown).
Then again, the greatest shows of the early Broadway era weren't as lightweight as people remember. Show Boat dealt fairly realistically with race relations, and not all of the good guys got happy endings. Rodgers and Hammerstein? Hooboy. Oklahoma! has a song wherein the hero tries to convince his rival to commit suicide, and he later kills his rival and is universally praised for doing so. The King and I has two self-righteous egos butting heads, and one dies at the end. The Sound of Music- yeah, real happy ending: they have to flee their home, leaving behind anything they can't easily carry, in order to escape the Nazis.
Whether William Shakespeare's plays are idealistic or cynical, and how much, is highly debated. The same plays can seem very different depending which critics you read.
Shakespeare'sRomeo and Juliet is utterly cynical toward romance as a whole, portraying the two Star-Crossed Lovers as blind to the reality of their family feud. Even though the two feuding families finally make peace with each other after the lovers are Driven to Suicide by their madness, it is still a highly cynical subversion of traditional love stories. You'd never know it, though, from listening to some of its very idealistic fans.
...Except that it's not, and you could make a strong case that the play is meant to illustrate the power of love (dumb and teenage though it may be) as a force for political unity. It's possible to walk away from the play with the message that even naive adolescent love can be an antidote to the impersonal hatred of political conflict. It's important to note that the opening sonnet says that Romeo & Juliet "doth with their death, buried their parents' strife"- implying that their deaths are directly, causally connected to peace, and that the resulting peace is as important to note as their deaths.
Urinetown, mentioned above, is a bit more complicated. It starts out as a pretty straightforward clash between the idealist and cynic, but when the cynic kills the idealist, the forces of idealism find a new leader who is both more idealist and more detached from reality, who blindly propels the story into a Nice Job Breaking It, Hero.
Cirque du Soleil shows are Earn Your Happy Ending at worst (see trope entry for examples), and shimmeringly idealistic at best. Saltimbanco was intentionally created to counter cynicism and despair, particularly regarding urbanization, in society. And Corteo takes the concept of the death-dream of a clown and turns it into a loving celebration of life.
Also, the characters themselves fall on different parts of the scale. Which happens to be heavily tilted towards cynicism. At the start, they range from midway through the cynical (Sweeney) to evil-but-not-either (Turpin) to falling off the idealist end (Anthony). By the end of Act 1, Anthony is about at the midway point, Sweeney's fallen off the cynical end, and Mrs. Lovett has actually risen into idealism. Once you hit the endgame, Antony is still at the midpoint, Johanna is obviously at the cynical end, Toby's, well, crazy, and Sweeney is a dot at the end of the cynical range. Mrs. Lovett seems to be the only one that actually becomes more idealistic.
The musical Man of La Mancha is practically a plea for idealism... which is quite the contrast with its original inspiration, Don Quixote, who is in the cynic side but moves the slide back and forth for the sake of the funny.
The musical Chicago announces its cynicism even before the curtain goes up:
"Ladies and gentlemen, you are about to see a story of murder, greed, corruption, violence, exploitation, adultery and treachery—all those things we all hold near and dear to our hearts."
The play The Time of Your Life has an entire paragraph, which can be found at the beginning of the script, stating the ideals which the principal characters live by.
Little Shop of Horrors starts in cynicism, quickly lifts into idealism, and then slowly descends to a level more cynical than where it started.
The Rise and Fall of the City of Mahagonny is cynical enough, but Kurt Weill's next opera, after he split with Bertolt Brecht, Die Bürgschaft, might be even more cynical. Just as a commercial dispute between the protagonist and his friend is about to be resolved with an Arranged Marriage between their children, the country is taken over by the Great Powers, who impose their law, which is the Law of Money and the Law of Power. Subsequently the country is visited by war, inflation, hunger and disease. While the poor become poorer, the protagonist is too busy making himself richer to look after his dying wife or his missing daughter. Comes the revolution, and his old friend shamelessly betrays him to the bloodthirsty mob.
Each Flaherty and Ahren show is a bizarre mix of each - the general idea is that it starts with some plucky, idealistic heroes, pushes them all the way to the other side of the scale, but ends on an extremely cheery note despite this.
In Ragtime, the main character, Coalhouse, goes from madly in love to slightly annoyed to enraged and murderous, only to end with him singing an entire song about hope and idealism, albeit after he dies.
In Once On This Island, the story begins with a lovely, happy young peasant girl, Ti Moune, falling in love with a rich man named Daniel. By the end of the show, she dies, heartbroken. But she turns into a tree, and spreads the power of love to everyone.
If you've ever read Dr. Seuss's Horton Hears A Who!, you know the basic plot of Seussical. A nice, spirited elephant named Horton discovers a world on a dust speck on a clover, and, of course, everyone thinks he's gone insane when he tells them. He goes through trials and tribulations, and almost has to watch the clover get boiled in Beezlenut oil. But in the end, everyone ends up believing that there really are tiny people on that dust speck, agreeing that "a person's a person no matter how small."
Charlie and the Chocolate Factory (the 2013 West End musical) takes place in a world so cynical that even children seem ready to cast off creativity and wonder in favor of ruthless, mindless materialism as soon as they're able, and as grumpy sweetstall owner Mrs. Pratchett puts it early on, "You get nothing for nothing in this world." Poverty-stricken, sweet, imaginative Charlie Bucket and his family watch in increasing despair as the Golden Tickets that grant entrance to the mysterious Wonka Factory fall into the hands of greedy, even underhanded brats. And then, a little luck comes Charlie's way when he finds the last of the five tickets. As it turns out, Willy Wonka is a Sugar and Ice PersonalityAnti-Hero who, though he's Ambiguously Evil and has No Sympathy for those who would let their greed get the better of them, believes wholeheartedly in the importance of wonder, beauty, and imagination. In his Cloud Cuckooland, the greed that pays off in the outside world leads to horrible ends, whereas Charlie's goodness and creative drive to make the world a better place for those around him ultimately grant him and his family an incredibly happy ending, making this a rare idealistic Black Comedy.