In The Things They Carried, what ideas in "On the Rainy River" are developed about the significance of idealism and truth in an individual's life?

Idealism, in general, is the pursuit of ideals unrealistically.  In literature, specifically, idealism is the opposite of realism.

Most of The Things They Carried is based on real life events in O'Brien's life, except "On the Rainy River."  It is the one story in the collection that is completely fabricated.  O'Brien never went to near-Canada or the lodge or the river.  There was no Elroy.  It is pure fiction, whereas most of the book is a mix of non-fiction, memoir, autobiography--all infused with fictional elements to "heat up the truth."  It's hardly idealism, though not exactly realism.  But it's still the truth.

So, does that mean "On the Rainy River" is not a true war story?  Of course not.  Remember, O'Brien says that a true war story is meant to be felt in the stomach.  The meanings of stories are truer than the realism of the events therein.  In other words: don't fall for the literalist's trap (it doesn't have to have happened to have meaning).  In fact, O'Brien says that story truth is truer than happening truth.

The truth is O'Brien was a coward; he went to war.  And the story brings that to life better than the way events unfolded at the time.

In the story, O'Brien must first show us how he was a coward.  He has to have Tim run away.  He has to use water symbolism.  He's got to have Elroy, the mentor on the quest.  He has to put O'Brien at a crossroads.  He has to give him a choice.  Only then can he tell us he was a coward at the end.  Fiction leads to the truth.

With that said, the only character in the novel that I find too idealistic is Elroy.  He seems too perfect, too wise, too much like the antithesis of Tim's father, too constructed as a mentor for the story's purpose to be completely believable.  The money.  The note.  All a bit too hokey to be believed.