I'm trying to understand why there are theoretical models predicting that spin and gravity should couple.
Specifically, what I'm asking is if such Standard Model extension comes from gauging the Poincaré group as per the Cartan variant of GR, where additionally torsion is sourced by spin instead of just energy and momentum.
Gauge field of local supersymmetry (=supergravity) - gravitino - leads to non-trivial torsion. Gravitino is a spin-$\frac{3}{2}$ field satisfying Rarita-Schwinger equation.
Update.
No, there is no violation of equivalence principle, since bosonic components of torsion still vanish. Whereas fermionic components give gravitino-matter coupling. See this answer for gravitino contribution https://physics.stackexchange.com/a/134689/85745
