Question: Did they like Oliver Cromwell, who founded a republic after a dispute about taxes led to the overthrow of a king, or did they see him as a usurping Caesar who destroyed a republic and became a tyrant?

Answer: 
Extemely short and simple answer: No, because for one thing, Cromwell eventually set himself up as dictator, the "Lord-Protector", which was simply a title for the person in charge. He first created a non-elected "representative" system before that, where the people in that system were simply nominated but not elected. In other words, he was very much like a Caesar, which started out with having a "Parliament" that he effectively controlled. The person(s) above goes into more detail, but that pretty much sums up why they wouldn't have a positive view of him. That said, ironically, one person who did have a positive view of him was Karl Marx, who viewed him as an early revolutionary.
I do think that the fact that Cromwell's sect of Puritans mostly emigrating to Massachusetts is part of the reason that the first shots of the revolution were fired there. There must have been, only a few generations later, a seething dislike of the crown. Think about supper table talk. No doubt that many were the grandchildren of people that fought in Cromwell's campaigns. Sympathy for Cromwell and his attitudes had to be present.