Why was Jeremiah treated well by the Babylonians? Jeremiah was persecuted, and all but killed by his countrymen, the Israelites. But when they were conquered by the Babylonians, he was rescued and treated well by the conquerors.1

Why is that? Was it because he predicted a Babylonian victory, so the Israelites saw him as a traitor and the Babylonians saw him as a "fellow traveler"? Or was it because the Babylonians saw "eye-to-eye" with him on matters of "righteousness," while the Israelites did not?




See the Wikipedia article on Jeremiah
I would suggest Jeremiah 1:7-8 and 1:18-19 as an answer. There we find that it is God who protects him wherever he goes. It wasn't the Babylonians' pity that stayed their hands; God Himself protected Jeremiah from them and the Israelites. 


  Jer 1:7  But the LORD said unto me, Say not, I am a child: for thou
  shalt go to all that I shall send thee, and whatsoever I command thee
  thou shalt speak.  Jer 1:8  Be not afraid of their faces: for I am
  with thee to deliver thee, saith the LORD. 
  
  Jer 1:18  For, behold, I have made thee this day a defenced city, and
  an iron pillar, and brasen walls against the whole land, against the
  kings of Judah, against the princes thereof, against the priests
  thereof, and against the people of the land.  Jer 1:19  And they shall
  fight against thee; but they shall not prevail against thee; for I am
  with thee, saith the LORD, to deliver thee.