with the following code (a boiled-down version of my original code)
#include
#include
template class A;
auto diff(A is the problem; regardless of anything else, if X and Y are different types, A and A are different types and cannot peek at each other's privates. Templates are not covariant!
The specific error here might be an eccentricity of GCC (in that it doesn't spot that X is the same type as Y) but the more general case where you might be trying to diff two different types (and why else would you have a separate template type in your diff function?) will never work, regardless of compiler.