Can a mix breed dog be signed up for KC obedience trials?

In the U.S. they can. In fact, in the U.S., all venues AKC, ASCA, UKC, have a mixbreed program where they compete alongside and earn the same titles as purebreds. Usually the requirement is that the mixbreed must be spayed or neutered. They are also generally listed as a "mixbreed" or as an "AMBOR", which is the "breed" club for mixbreeds here, it represents American Mix Breed Obedience Registry, they also require all mixbreeds to be spayed/neutered.