Is it a
Two way traffic sign?
I may be yellow; two-faced I be,
It is yellow, with arrows facing in two directions
But you would be wise to never cross me.
To cross can mean "to oppose openly", that wouldn't be a wise thing to do as you might run into oncoming traffic
I stand straight and tall; my authority's given.
It's a sign usually affixed to a straight and tall pole, and since it is a road sign, its authority is given by law
You'd best follow me if you're want to stay livin'.
Seems obvious, same as the second line, you might run into oncoming traffic if you don't follow the sign
Is just reinforcing the message
A number of answers are like signs pointing us in the right direction; a number are not. Probably refers to the answer being a "sign pointing us in the right direction".
About the title:
It's all G
reek to me
Might refer to the title about palindromically calling it "IDDI" being far-fetched/hard to understand Refers to the fact that the sign is made up of iota's (Ι) and delta's (Δ) from the Greek alphabet.
In this picture, the left side would be
but the right side would be
Seems to show to a road with directional lanes swapped from right to left, so the left side could be "Inverse (or Inverted) Direction" (which is the same as opposite direction), if left is the "Inverse Direction" (ID) then the right side would be palindromically be "Directionally Inverse" (DI) and vice-versa when the lanes are swapped. And yes it is far-fetched/hard to understand why anyone would actually palindromically call it "IDDI", but I guess you could.. If you looked at the sign in the Greek alphabety way, you could palindromically call it "IDDI", because the sign is made up of "ΙΔΔI".