Not so. Elementary particles of the same type are proven to be identical by the symmetry they display, and the result is the entire structure of matter, for a start.
Quantum Fermi-Dirac and Bose-Einstein statistics, respectively for fermions e.g. electrons and bosons e.g. photons, are different from classical Maxwell statistics precisely because the particles are identical. That means that if you exchange any two particles, the observables have to remain the same, which means that the wave function has to remain the same except for a phase shift. (Observables aren't directly sensitive to the phase shift, though it can be measured.)
Fermi statistics are responsible for the existence of solid matter at ordinary density, owing to the Pauli principle. Pauli showed that the antisymmetry of fermion wave functions under exchange (i.e. they change sign when you exchange electrons) leads to the wave function vanishing if you try to have more than one electron per state. (Two if you count spin.)
If electrons weren't identical fermions, i.e. they obeyed Maxwell or even Bose-Einstein statistics, everything would collapse to nuclear density if not higher. (The density of the nucleus is also set by the Fermi statistics of the nucleons.)
So it isn't exactly blind faith. ;)
Cheers
Phil Hobbs