We study the impact of the loss of axial symmetry around the optical axis on the polarimetric properties of a telescope with segmented primary mirror when each segment is present in a different aging stage. The different oxidation stage of each segment as they are substituted in time leads to non-negligible crosstalk terms. This effect is wavelength dependent and it is mainly determined by the properties of the reflecting material. For an aluminum coating, the worst polarimetric behavior due to oxidation is found for the blue part of the visible. Contrarily, dust -- as modeled in this work -- does not significantly change the polarimetric behavior of the optical system . Depending on the telescope, there might be segment substitution sequences that strongly attenuate this instrumental polarization.