BEIJING—Supporters of ousted political leader Bo Xilai are turning up the note of political discord in China with increasingly loud criticism that the policies of current Communist Party leaders are widening inequality and breeding social unrest.

The movement, known as the new left, remains relatively small and obscure, and is unlikely to have a major impact on the coming shuffle of party leadership positions. But criticism from Communist hard-liners in the era of online social media places China's leaders in a tricky position...