Maintaining VFR altitudes when following N/S roads/rivers

Mxsmanic wrote:
If you are following a road or river or other feature on the ground
while flying VFR, and that feature runs north/south but often veers
off to one side or the other, are you expected to change your altitude
each time you move from a heading of 0-179 to 180-359 or vice versa?

You appear to familiar with FAR 91.159. There are two aspects you didn't
make clear in your hypothetical question that determine whether it can be
answered objectively: whether the aircraft is more than 3000 AGL and
whether the aircraft is maintaining level cruising flight. Once you have
those answered you should be able to answer the question yourself.