Question

Can literary movements share ideas concerns or characteristics

Answer 1

Of course literary movements can share ideas, concerns, or characteristics.
Romanticism shares many of its ideas with ancient Greek and Roman literature; Classicism is influenced by Classic literatures; Postmodernism is a response to Modernism, but it shares some of its characteristics.
Although each literary era is created as a negative response to the era which preceded it, still there are many movements which share the same things.