Why did the English people differ in their views on the execution of Charles I?

Charles I was a bad king who believed in the divine right of kings and thought that he had absolute power when he arrested members of Parliament. He had totally forgotten or ignored the provisions of Magna Carta which limited the king's power and gave power to the barons (loosely speaking, Parliament) It was this arrogance that brought about his eventual execution.

Killing a king was alien to the British people and was a measure of just how bad, and unpopular Charles was. So, the lack of mass protests, demonstrations and rescue attempts shows that public opinion was in favour.

Only the defeated Royalists were against this action and they were basically the privileged ones who benefitted from the king having such power.

Unfortunately, Cromwell's Commonwealth (Republic) were no better and went to the opposite extreme - and they destroyed a great deal of British history and architecture.

It would have been better all round had Charles been humiliated, like John before him, but remained king with reduced powers. This would have reinforced Magna Carta and done just as much to push Britain along the path of Constitutional Monarchy and ultimately Parliamentary democracy.