Father Wiggly versus The Herecat. How to keep two cats from fighting?

My cat, Father Wiggly, has been having serious theological disputes with a neighbor's cat who entertains a rival metaphysics. Both cats agree on the general point that the way to Salvation for birds and small animals runs through the tummy of a cat, but they disagree on which cat's tummy is the right one. It seems that at some point in their discussion the cat-word for "blasphemer" is used, and then the fur starts to fly. I only let Wiggles outdoors to use the restroom, yet these cat-debates have been increasing in frequency. How do I put an end to them?