If the proton and muon sizes were different [...] They are different, in fact the muon is believed to be a point particle and not to have any internal structur

If the proton and muon sizes were different [...] They are different, in fact the muon is believed to be a point particle and not to have any internal structure like, for example, the proton. Nonetheless one can assign a non-zero radius to the muon in specific contexts due to its interaction with the vacuum.