Staggered, Karsten-Wilczek (KW) and Borici-Creutz (BC) fermions all retain a remnant chiral symmetry. The price to be payed is that they are doubled, and the resulting taste symmetry is broken by cut-off effects. We measure the size of the taste symmetry violation by determining the low-lying eigenvalues of these fermion operators in the two-dimensional Schwinger model which admits, like QCD, a global topological charge $q \in \mathbb{Z}$ of a given gauge configuration. We find that it matters whether the pertinent eigenmode is a would-be zero mode or a non-topological mode. The intra-taste splittings of these fermion formulations are all found to diminish with increasing $\beta$. Our goal is to verify standard Symanzik scaling for these taste-breaking effects.