The increased capabilities of coupling more and more materials through functional interfaces are paving the way to a series of exciting experiments and extremely advanced devices. Here we focus on the capability of magnetically inhomogeneous superconductor/ferromagnet (S/F) interfaces to generate spin-polarized triplet pairs. We use the power of the Josephson effect for a quantitatively accurate proof of the coexistence and tunability of singlet and triplet transport in ferromagnetic spin filter junctions. We build on previous achievements and find unique correspondence between neat experimental benchmarks in the temperature behavior of the critical current and theoretical modeling based on microscopic calculations. This turns to be a unique opportunity to model disorder and spin-mixing effects in a Josephson junction (JJ) to enlarge the space of parameters, which regulate the phenomenology of the Josephson effect and could be applied to a variety of novel types of JJs.