When riding 2005 fuel injected harley road king, engine pops, backfires, and idles fast, why?

Sounds like the intake manifold is leaking. The area where the leak usually happens, are those two rubber sleeves that go from the heads, (Cylinder heads) to the intake. Sometimes the clamp/s loosen up. Sometimes these rubber sleeves deteriorate, and cracks form.

This makes the engine backfire, pop, and idle fast.

The added air at the wrong time cause a backfire, when you let off the throttle. The added air causes the engine to pop, because the exhaust valve has sucked up some cold air.
The engine idles fast, because more air is being introduced, and not metered by the injection system.

(The exhaust valve thing. Exhaust valves are supposed to open, and let exhaust out right? Well there is a thing called Valve Overlap.
The Exhaust valve hasn't closed all the way yet, and the Intake valve is opening.
The 4 stroke engine, (Of which a Harley is), has these four strokes.
1.Intake Stroke. Fuel/air is sucked in.
2.Compression Stroke. The piston comes up and squeezes the fuel/air mixture.
3.Combustion Stroke. The spark plug lights the fuel/air mixture off.
4.Exhaust Stroke. The spent gases are expelled out.

Your Road King has one camshaft. There are four cam lobes on it.
Intake, Exhaust, Intake, Exhaust.

If you had the camshaft in your hand, and had the gear end facing you, look down the camshaft. You will see those egg shaped cam lobes. You will notice that No.1 cylinder Intake lobe is facing to the left.
No.1 Exhaust is facing to the right.

If you put a degree wheel on the gear end of the camshaft, and had the No.1 Exhaust lobe ramp nose facing straight up, you would see that it's about 110 degrees, before the Intake lobe ramp at .050 lift, comes into play. (The roller, of your roller lifter has raised the Exhaust valve up .050 inch) There is about 55 degrees before the Exhaust valve hasn't quite shut.
This is okay for normal running. Introduce a vacuum leak, and the surge of extra cold air, makes it pop.

Solution? I suggest checking to see if the clamps on those rubber sleeves are loose. You can also spray WD-40 towards the ends of each rubber sleeve, when the engine is idling, and see if it speeds up. Means, one or more, of those rubber sleeves has deteriorated.