the statistics of a collection of particles, ie fermions or bosons, depends on their symmetry under commutation. that is, the wavefunction of the collection of particles, which does have physical meaning isofar as its square is the real density of the particles, must also obey this symmetry, ie it must negate (-1*) under exchange of two identical fermions. so it's not that the 'fermion' cares, but that the consequence of (anti)symmetry under exchange affects the density of a collection of such particles, which leads to a measurable difference in their statistics (how likely they are to be close to each other) compared to non-symmetric (normal) counterparts.
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