The sex offenders list protects children and young families by identifying men and women (mostly men) who have a sexually motivated criminal record, be it rape or pedophilia and etc. 

A pet offenders list would essentially bar the sale, adoption or ability to sell pets for reasons such as animal cruelty or fraud involving pet sales. This would be useful in closing shelters and rescues that have no more than a view for profit. 

This happened to my family and a bunch of other people on Facebook through a serious rehoming and sale group, costing thousands of dollars in total. 

If such a list could be compiled, this would be a way to protect families who want a companion animal, allowing them to have no fear in putting money they may not have forward to allow their family to know the joy of pet ownership.

At the same time, it may restrict the purchase and/or adoption of any animal, providing that the home is as healthy for them as it would be for any other member of the family.