Harry told Snape that Lily only liked James because of his money and looks. So is it that Snape now thinks his students only like him because of his position and power, whereas before he thought they liked him for who he was? Has he become even more cynical? More inclined to reject people?

This is what I figured. And there was the comment by Dumbledore (or Minerva?) that Snape wouldn't hurt Harry because Snape loves Harry's mother. So I'm now assuming that Harry managed to convince Snape that Harry's mother is not love-worthy, which means that Harry is now stripped of that protection.