I disagree with the above answers.
Our visual culture and the century of cinema has dictated that we evaluate a 180 degree shutter as "normal", because that is how film cameras have worked almost forever, and that is how most scenes in every movie are shot.
180 degree shutter is the same as 1 over twice the frame rate, or 1/48 for 24fps.
If there is little to no movement in frame, it is true that shutter speed will not create any visible effect, but with fast character movement or almost any but the slowest camera movement a different shutter speed will be noticeable.
It is valid to say that for storytelling reasons you need the shutter to be closed down, but if its just for technical reasons, it will be noticed, and will come through as amateurish. Use ND filters for exteriores, for sure. If you are afraid of quality loss, test them, but every major production uses ND filters, so unless you use cheap plastic ones, you will be fine. Be more wary of color cast than of resolution loss though. Some digital sensors need extra IR filtration on hot day exteriors to maintain color consistency.
Regarding timelapses, the same rule applies. Use 180 degree shutter unless the story calls for something different. This presents an extra challenge. If you need one frame every 10 seconds, it means that each frame must be exposed for 5 seconds, which is a lot for day exteriores, and you will need a lot of ND filtration. I am sure there are many great timelapses that do not follow this rule, but I suggest looking at Kooyanisqatsi, the feature film that made nature timelapses famous. Every shot uses a 180 degree shutter, and it looks gorgeous, cinematic, epic.