The answer depends on where the series falls in the Sliding Scale of Idealism Versus Cynicism.
A story can be idealistic or cynical towards any idea. In general, if the story values or is hopeful for a particular ideal, then it is idealistic. If the story criticizes or assaults that expectation, then it is cynical.
For a simple, archetypal example, let's assume that the idea to believe in is Humans Are Good/Rousseau Was Right. In idealistic series, those who believed it got lots of friends and a Happy Ending (therefore, Right Makes Might), while cynical series are Crapsack Worlds where those who believed it got ruthlessly bullied by everyone else (therefore, Might Makes Right). Of course, the definitions of "Right" and "Crapsack" in the above can technically mean whatever one wants them to mean.
However, be careful not to confuse idealism with straw optimism, cynicism with straw pessimism, and the scale as a whole with the Sliding Scale of Silliness Versus Seriousness. Also note that when this applies to characters, this does not mean good or evil. After all, it's perfectly possible for an idealist to be evil, and a cynic to be good. Likewise, a very cynical series could be quite lighthearted (see also: Crap Saccharine World), conversely a very idealistic series could be extremely dark. It's also true that comedies can be cynical as all hell, and dark dramas or brutal deconstructions can end idealistic (see also: A World Half Full).
See also: The Idealist and The Cynic for the archetypal characters. For how both sides often portray each other, see Wide-Eyed Idealist/Silly Rabbit, Idealism Is for Kids, and Grumpy Bear/Silly Rabbit, Cynicism Is for Losers. See Cynicism Tropes, and Idealism Tropes for lists of each.
No real life examples, please; This particular sliding scale can be the topic of fierce debate. Each person will have a different point which they tend towards. Therefore, this scale is most useful in targeting demographics and those who are sympathetic to a certain world view, and identifying where on the spectrum one's own work is.
Cerebus Syndrome describes a shift from comedy to drama and this often also results in a shift from idealism to cynicism. Reverse Cerebus Syndrome is the inversion. When shows Zig Zag between the two, they're on a Cerebus Rollercoaster.
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