By Uncle Al who has submitted a #400,000 screenshot.
Does the Equivalence Principle have a parity violation? Weak interactions (e.g., the Weak Interaction) routinely violate parity conservation. Gravitation is the weakest interaction.
Either way, half of contemporary gravitation theory is dead wrong.
Gravitation theory can be written parity-even or parity-odd; spacetime curvature or spacetime torsion. Classical gravitation has Green~Rs function Newton and metric Einstein or affine Weitzenböck and teleparallel Cartan. String theory has otherwise and heterotic subsets. Though their maths are wildly different, testable empirical predictions within a class are exactly identical...
...with one macroscopic disjoint exception: Do identical chemical composition local left and right hands vacuum free fall identically? Parity-even spacetime is blind to geometric parity (chirality simultaneously in all directions). Parity-odd spacetime would manifest as a background pseudoscalar field. The left foot of spacetime would be energetically differently fit by a sock or left shoe compared to a right shoe.
String theory could be marvelously pruned. Does a single crystal solid sphere of space group P3(1)21 quartz (right-handed screw axes) vacuum freefall identically to an otherwise macroscopically identical single crystal solid sphere of space group P3(2)21 quartz (left-handed screw axes)? Both will fall along minimum action paths. In parity-odd spacetime those local paths will be diastereotopic and measurably non-parallel -- a background left foot fit with left and right shoes.
A chiral background pseudoscalar field diverges Big Bang evolution of matter and antimatter. It sources biological homochirality (exclusively left-handed chiral protein amino acids and right-handed chiral sugars). At a 10^(-10) difference/average or smaller level it is consistent with 420+ years of physical observations.
The world has lots of Eötvös balances with 10^(-13) difference/average sensitivity. The proper challenge of geometric gravitation is test mass geometry. More than 2100 tonnes of single crystal quartz are grown annually. Somebody should look.