Bremsstrahlung radiation involves accelerating electric charges through non-zero electromagnetic fields. When all charged particles are accelerated by gravity

Bremsstrahlung radiation involves accelerating electric charges through non-zero electromagnetic fields. When all charged particles are accelerated by gravity in the same way by a [close to] uniform gravitational field then they are not being accelerated through non-zero electromagnetic fields because the causes of those fields are also accelerating in the same way. However, if an electron were falling into a charged, rotating black hole then I'd expect some Bremsstrahlung radiation indeed. That said, IANAP. And when I say "accelerated by gravity" I am taking the interpretation that gravity is a force, which is a valid interpretation (see other commentary above).