I am not sure I follow. unsigned types in C are residues and not binary polynoms or Galois fields (also you can of course store them in unsigned integers).

The conversions work, e.g. conversion to a smaller unsigned type are reduced. That some other conversion work does seem convenient to me and not a problem.

One can, of course, define types in C for Galois fields and access them using functions that do the correct operations (and by wrapping it in a struct one can also prevent regular operations to be used on such type). In C++ one can overload the builtin operators, but I am not terrible sure this is even a good idea.