A cylindrical projection with a vertically oriented cylinder which is tangent to the Equator produces a map that you are looking for. In this kind of map projection, all the points on the same latitude (all the points that are at the same distance from Equator) stays on the same horizontal line on the projected map.
Found in https://twitter.com/amazingmap I can't personally vouch for accuracy.
From tweet, several complaints about Antarctica, "wrong pole", etc.
New favourite map projection. Hellereal Boreal Triaxial Projection
World Mercator map projection with true country size and shape added #Map #Maps #Amazingmap #Amazingmaps #Mercator