Shelley was indeed a late Romantic who, perhaps more than any of the other Romantics, was outraged by the political and social conditions of his country. In his youth he was an atheist, and throughout his life he held controversial opinions. If you want to see how radical Shelley can be in some of his writings, take a look at "A Song: Men of England" and "England in 1819." These are very vigorous political poem that leave no doubt about the kind of politics they express.
Shelley is a Late Romantic who, like many of the Romantics, saw the goodness of people, the importance of recognizing our innocent humanity, and wanted emotional truth to be at the core of good writing. He is known for being liberal in his literature and his politics. In his sonnet "To Wordsworth" he even comments on poetry that are "songs consecrate to truth and liberty." His poem "England in 1819" is about the poor way people are living and is almost a call for revolution.
Shelley was one of the Victorians. Many of the Victorians desired to not just reflect society in their work, but hold a mirror up to it that would show people what needed to be changed. Like Dickens, and Mary Shelley for that matter, Shelley intended to demonstrate there were factors of society that needed change.