Most scholars agree that the writings of Plato have two periods: the first is where he is merely repeating the words of Socrates, and the second is where he is expounding his own views. Most also agree that the Republic is in this second category.
Plato begins with the assumption that the purpose of art is to help in the training of the philosopher-kings of the ideal state. Rightfully, he excludes things such as indecency and erroneous depictions of God from art. There are also some more doubtful exclusions.
Anthropomorphism God is not anthropomorphic.
Laments/Comedies/Drinking songs These things are not conducive
to the training of leaders;
they are irrational/dangerous.
Imitation/Pantomime By imitating a thing, one becomes like it.
Perhaps others that I cannot remember.
Plato's fallacy is the assumption that just becuause these things are what they are, that they will have the psycological effect he thinks they will have or becuause they are dangerous/useless, they should not be. But no child ever really became more like a dog because they pretended they were. And the sorts of things that he forbids are all legitimate human activities: Crying, laughing, drinking, etc. Their absence could be worse than what is prevented by their absence, an aspect Plato never even imagines.
Plato's other repbulican aesthetical views, however, are very sensible. They consist in the fact that that beauty and truth and goodness are allied, and that by seeing beautiful things, one can learn to recognize what beauty is, and that this is conducive to goodness.