Cromwell helped create a republic (called the commonwealth) after the execution of Charles I in January 1649. From 1653 to his death in 1658, Cromwell ruled as Lord Protector of the British Commonwealth.
Establishing a republic meant there was no monarchy. This was a very radical move in that time period. The prevalent belief was that power on earth descended top down, from God in heaven through God's anointed king or queen. From there, power extended in greater chain of being, to the aristocracy and then to the people. A government derived from the will of the people seemed to many a violation of God's plan for the world. To some groups, such as the Quakers, the execution of the king signaled the Second Coming of Christ: with the monarch removed, the Quakers (and other radical religious sects) thought Christ was soon to arrive to rule the earth himself.
Instead, they got the military leadership of Oliver Cromwell.
Cromwell actually treated the dissenting religious groups with a higher level of tolerance than they had met with before the Civil War or would meet with for decades after the restoration on the monarchy. Cromwell did not want to rule as a military dictator and supported England's first-ever written constitution, The Instrument of Government. This document made the position of Lord Protector an elected position, rather than hereditary one, although the person so elected held the position for life.