  We extend the recent rigorous convergence result of Abels and the second
author (arXiv preprint 2105.08434) concerning convergence rates for solutions
of the Allen-Cahn equation with a nonlinear Robin boundary condition towards
evolution by mean curvature flow with constant contact angle. More precisely,
in the present work we manage to remove the perturbative assumption on the
contact angle being close to ninety degree. We establish under usual
double-well type assumptions on the potential and for a certain class of
boundary energy densities the sub-optimal convergence rate of order
$\smash{\varepsilon^{\frac{1}{2}}}$ for general contact angles $\alpha \in
(0,\pi)$. For a very specific form of the boundary energy density, we even
obtain from our methods a sharp convergence rate of order $\varepsilon$; again
for general contact angles $\alpha \in (0,\pi)$.
  Our proof deviates from the popular strategy based on rigorous asymptotic
expansions and stability estimates for the linearized Allen-Cahn operator.
Instead, we follow the recent approach by Fischer, Laux and Simon (SIAM J.
Math. Anal. 52, 2020), thus relying on a relative entropy technique. We develop
a careful adaptation of their approach in order to encode the constant contact
angle condition. In fact, we perform this task at the level of the notion of
gradient flow calibrations. This concept was recently introduced in the context
of weak-strong uniqueness for multiphase mean curvature flow by Fischer, Laux,
Simon and the first author (arXiv preprint 2003.05478).
