Four-dimensional \( \mathcal{N} \) = 2 supergravity theories become rigid in gravity-decoupling limits. We study this effect for type II string compactifications on general Calabi-Yau manifolds, focusing on vector-multiplet trajectories whose endpoints exhibit axionic shift symmetries. This comprises field excursions of both finite and infinite distance, but the latter display specific features due to the appearance of light towers of extremal BPS states, in agreement with Swampland principles. We show that vector multiplets split into two sets: those with gravitational and with rigid mutual interactions, and that only a subset of the latter — dubbed core RFT — can fully decouple from gravity. We characterise the core RFT in terms of the axionic shift symmetry, and derive decoupling criteria based on kinetic and Pauli interaction mixing. Our framework is illustrated in large complex structure, conifold-like, and Seiberg-Witten limits. In the last case, Pauli mixing obstructs decoupling whenever the dyonic and extremal BPS towers appear at the same scale. Across all these examples, the decoupling from gravity is signalled by a divergent moduli-space scalar curvature.
