Not A Teacher
The phrase of "cold entrails of a kill with you" refers to the habit of a pet cat to bring home dead animals such as mice and birds and leave them where you might find them. The writer is comparing this to the sacrifices left in some religions for their God or Gods.
Entrails is a synonm for guts, intestines and other internal organs, "a kill" refers to the dead animal and "with you" means that the cat is willing to share the creature it has killed with you its owner.
Just out out of curiosity is this a quote from the late Sir Terry Prachetts book "The Unadulerated Cat?"
Student or Learner