Steve,
Animals were put on this earth for our use. Turning them into glue, clothes, shoes, belts or food doesn't bother me one tiny bit.
That old hide glue can be an absolute bear to get off too. Sometimes it just decays and falls apart, then 2" over it's still rubbery and holds like a C-clamp.
The Elmers carpenter wood glue is one of my favorite glues. I've not had anything come apart that I've glued with it. Not yet anyway.
Joe