I'm going to assume (spoilers) that people got teary over the scene where Po realized he was in the destroyed village where he was born and had to make peace with the fact that his family was murdered, so he would never (as far as he knew at that time) get the closure of meeting them.
I didn't see anyone crying when I went to watch it, but I do know people sometimes draw on their own experiences, like folks who watch UP and cry because they think of a lost loved one, or people who watch Inside Out and ... think of their first move, I guess. Or whatever else made their innocence / optimism die.