How common was pro-Republic sentiment in the Roman Empire?

by Salgados

Some scholars claim that Tacitus held republican sympathies and Robert Graves makes the Emperor Claudius seem like a closet republican. Was there a longing among intellectuals or the public for a return to the Republic? How vocal or popular were republicans, and how long into the Empire did these feelings last?

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Follow up: How much did the average person ca. 300 know about the political history of Rome? Did they understand the differences between the Empire and the Republic? Did they even know it used to be a Republic?