While studying James and Charles, I came across the significant public opposition to religious innovation towards arminianism; arguably being a significant motivator for the civil war.
How is it then, that Henry was able to make such a drastic change without opposition. Or perhaps, having not studied Henry VIII's reign, I am mistaken and he did face much opposition?
I'd take issue with the characterization of Charles' policy as an innovation -- he wasn't a Calvinist, and that got him in trouble with Parliament, which wanted more innovation, at least in terms of worship and theology.
Check out Eamon Duffy's book the Stripping of the Altars for a good treatment of King Henry's time. The common people of England were significantly resistant to religious innovation, but few powerful men stood up for that side of things. (Thomas More is regarded as highly strange for getting himself martyred over the Oath of Supremacy.) Add to that the money and land to be gained from dissolving the monasteries, and the aristocracy had a material reason to be interested in abolishing the Roman hierarchy.
From Elizabeth on, the only relevant divisive questions were two: what flavor of Protestantism the Church of England should practice, and what degree of tolerance to offer non-conformists. The middle class (supposedly represented by the House of Commons) favored Puritan Calvinism and no tolerance for non-conformists. Charles' attempts to preserve the Elizabethan and Jacobean status quo of the via media in worship earned him Parliament's opposition, and his attempt to impose that same status quo on the Presbyterian Church of Scotland via the Book of Common Prayer earned him Scottish opposition en masse.
So the Scottish nobles and commoners rebelled against him for his innovative clampdown on religious liberty, while the "Roundhead" wing of Parliament turned on him for his conservative stance on actual worship in the Anglican church.
The common people of England continued to be ignored.