We study ultralight scalar fields with quadratic couplings to Standard-Model fermions and derive strong constraints from white-dwarf mass-radius data. Such couplings source scalar profiles inside compact stars, shift fermion masses, and can produce a new ground state of matter. We analyze couplings to electrons and to nucleons, incorporating composition and finite-temperature effects in white dwarf structure and equations of state. We identify two robust observables: (i) forbidden gaps -ranges of radii with no stable configurations — and (ii) characteristic shape distortions that drive white dwarf masses toward the Chandrasekhar limit (electron couplings) or shift the maximum mass (nucleon couplings). Confronting these predictions with precise measurements for Sirius B and Procyon B, together with the global white dwarf population, excludes large regions of unexplored parameter space and extends earlier QCD-axion-specific bounds to a broader class of scalar theories. Our stellar constraints rely only on sourcing and do not assume the scalar constitutes dark matter; where mass reductions are small, precision laboratory searches remain competitive. White-dwarf astrophysics thus provides a powerful, largely assumption-minimal probe of ultralight, quadratically coupled scalars.