In other words, can mismatched particles and antiparticles react with each other? What about an up quark and anti-down quark?
A left-handed up quark and a left-handed anti-down quark can annihilate into a W boson because of the nature of the weak interactions. Right-handed quarks do not interact via W boson because W boson is only left-handed, so they will not annihilate each other.
On the other hand, electron and an anti-muon can not annihilate each other in tree level because it would violate lepton number conservation. They can interact via a W boson but also an electron neutrino and a muon anti-neutrino would be created in the process.
There are some Grand Unification theories that allow lepton number violation and predict a rare process of annihilating electrons and muons into some new kind of bosons.