What does this quote mean from "By the Waters of Babylon?" "Truth is a hard deer to hunt. If you eat too much truth at once, you may die of the...

To me, when John's father says this, he is referring to
the idea that truth can be harmful to people whose faith contradicts those truths.  In
other words, if you have a faith that says one thing, you can be hurt (spiritually) by
truths that contradict what your faith tells you.

In this
story, John and his father are (or are going to be) elite priests who know things that
the people do not know.  They keep some secrets from the people so as not to damage the
people's faith.  In the quote that you cite, John's father is telling him not to reveal
too much truth (all the things he learned when he went across the water) for fear that
it will hurt the people's faith.