How militarily important were Patriot militia forces the American Revolution? A popular narrative portrays the war as a victory of persistent and wily citizen-riflemen against a professional military, but how accurate is this?

It's a gross oversimplification stemming from some romanticization since the 19th century. While militia were important to both sides, a lot of the major battles were won between two professional armies, not just the militia against the British army. To say the militia did the brunt of the work is really dishonest, especially to the soldiers of the American Continental army -who were the professional soldiers. Most of the rifleman mythos comes from the battle of King's Mountain, featuring rifle-wielding frontiersmen against Loyalist militia, but not every determining battle was like that, especially in the southern campaign. Charleston, Camden, Guilford Courthouse, Siege of 96, Fort Motte, Yorktown; these featured linear warfare and were decisive battles of the war.

Yes, you battles like King's Mtn, Ramsour's Mill, and others that featured mainly militia on both sides but they're not wholly representative to the war. Not to mention, smoothbore muskets were more commonly used on both sides, not rifles. Both sides did have soldiers that used rifles, but they did not make up a majority of the army. Rifles were not as fast to reload, taking between 1-2 shots a minute versus 3-4 with a musket, and were not as reliable, nor could they be used as a bayonet. They were mainly used for skirmishing tactics.

For the most part, mainly of the high ranking officers on both sides did not have a high opinion of militia. They were prone to run, not super dependable due to the nature of militia; though they did have their moments like King's Mtn. In the Carolina Campaign, militia was pretty important in bolstering Continental forces due to capture of many Continental regiments after Charleston. Much of the fighting in the Carolinas were done between militia groups, but most of those engagements were on the small scale.

In short, militia though important did not singlehandedly fight off the British.

Sources:

Matthew Spring's With Zeal and Bayonets Only (does a great job of a telling how the British army adapted to American terrain and tactics)

Lawrence Babit's Long, Obstinate, and Bloody

Middlekauf The Glorious Cause

Papers of Nathaniel Greene

Christopher Geist Of Rocks, Trees, Rifles, and Militia

Edit: Forgot another useful reading [article](https://allthingsliberty.com/2013/12/militia-continentals/)