How Important is the 180 Degree Shutter Angle Rule?
The "180 shutter speed rule" you mention is only about setting your shutter speed at about double your camera's frame rate. It is not about actually shooting with a 180 shutter speed no matter what.
So, if I shoot at 25 fps, I'll set my shutter speed at 50 (because I like my footage to look more natural -- without the strobe-like effect that comes with high shutter speeds). If I were to shoot slow motion though, I would opt to shoot at, say, 50fps and set my shutter speed at 100 (to get crisper slow motion footage), and so on and so forth.
There is not relation between the "golden hour" and shutter speed. You can shoot during that time of day, or any time of day, with whatever shutter speed you pick, provided there is enough light.
ND filters are really used to control depth of field when using a wide iris/aperture on your lens in bright conditions (like an f2.8 or wider in the middle of the day).
This is a good, clear break down of shutter speed use in video: