How to align shapefile layers

I currently have a problem where my shapefile layers do not align, is there any way to get them to align without changing the shapefile itself?

These are meant to be the same islands/area, but they do not align

I'm using a third-party coastlines shapefile dataset(https://www.naturalearthdata.com/downloads/50m-physical-vectors/), as the Matlab one just didn't include half the islands in my 1x1 square. This high res one is still missing an island. (left image)

I'm also using a third-party roads shapefile (https://sedac.ciesin.columbia.edu/data/set/groads-global-roads-open-access-v1/data-download) for the same reason.

using a hgt file for the topography on the right, which I've read in and I'm using MeshGrid for