Mass and spin are invariants under spacetime transformations (Lorentz transformations); charges are invariants under transformations that commute with the former-they're ``internal'' transformations. The only exception that allows any ``mixing'' between them is provided by supermultiplets-a loophole of the Coleman-Mandula theorem. However this doesn't imply that charge and mass are related in the way proposed; it implies that particles in the same multiplet have the same mass and the same charge. It doesn't relate the two quantities.
Neutrinos carry weak charge-that's how they interact with other particles. Charge isn't exclusively ``electric'' charge. And, incidentally, the Higgs has (weak) charge, that's how the Yukawa couplings are realized, but doesn't have spin.