Since its start as a holy celebration in the second century, Easter has had its non-religious side. In fact, Easter was originally a pagan festival. As it happened, the pagan festival of Eastre occurred at the same time of year as the Christian observance of the Resurrection of Christ. The festival was altered, to make it easier to convert Pagans to Christianity. The early name, Eastre, was eventually changed to its modern spelling, Easter.
The Easter Bunny is not a modern invention either. The symbol originated with the pagan festival of Eastre. The goddess Eastre's earthly symbol was the rabbit. So the Easter bunny has its origin in pre-Christian fertility lore. The first "modern" written account of the Easter Bunny was mentioned in German writings in the 1500's.
Eggs were also seen during the festival of Eastre as symbols of rebirth and spring, thus the the Easter Egg. Now I am not sure how or why the legend of a rabbit laying eggs came to be, but it seems to have been a legend that was around since the 1680's. Children would make a nest for the bunny to lay eggs. That nest is now the modern day Easter Basket.
So that is it in a nutshell or should I say egg shell!?!? It doesn't matter if your religious or not, eggs or no eggs. Easter is a holiday for everyone and can be celebrated as YOU see fit. As for my Jewish friend, hope some of this helps clear up the mystery of the "egg pooping" bunny!