Ingersoll's metaphor "every beautiful thought is a teacher" affects the meaning of the interview in the following way:
It conveys the idea that people can learn from the thoughts they have.
Ingersoll is talking about the effect a play can have on an audience, and since a play is a form of art and it can make people think and reflect upon countless topics and issues, it can also lead people to have beautiful thoughts and consequently learn from them, since those thoughts are teachers in Ingersoll's point of view.