What was the historical and political significance of the Mayflower Compact?

Not much, actually. Those who migrated to the Massachutsetts colony (the Pilgrims and the Puritans) originally were religious fanatics who had very little to do with the later history and political development of the nation. /The charters of Virginia, Maryland, and Pennsylvania, for example, were much more the basis for the American system of governance.

The Pilgrims were romanticized much later in magazines and such, especially in promotions around the Thanksgiving holiday.