1) Protons are not fundamental particles; muons are. Proton characteristics arise from those of quarks, and perhaps gluons.
I’m assuming by “have parity” you mean “conserve parity.” Muons violate parity conservation because they decay by the weak interaction. When the weak force is not involved in a nuclear reaction, parity is conserved.
2) One possible explanation is that particles not described by the Standard Model are involved in the muon decay, and their presence affects the measured value of the muon magnetic moment.
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