Artificial.
Depicted: Emmeloord which is built on a polder - lands taken from the sea. The resulting engineered shorelines are straight because of the convenience of building in straight lines.
The Dutch are famous for this and these are the long straight lines requested from the OP. But the Dutch do not have a monopoly on this. Here are similar obviously artificial shoreline from Tokyo. Some of these are reclaimed lands and some were made to facilitate human use.
These artificial straight line shores are not some sort of fractal. To my eye they seem pretty random. It is not such a stretch to think that a planet inhabited by intelligences not unlike us might similarly engineer their shorelines.
They will not stay straight without maintenance. If they are not maintained the water will wear them into nonlinear shapes again. Unless the water also disappears. I found this city on what used to be the shore of the Aral sea.
