Antimatter is generated at extremely high (relativistic) speeds and generally has to be slowed down ("cooled") in order to make careful measurements or to even collect multiple particles together. And that can't be done unless you can steer the particle with electromagnetism.

If you just generated individual relativistic anti-neutrons and tried to watch them follow ballistic trajectories in gravity, I suspect they'd just look like perfectly straight lines up to the limits of your detector resolution. Not sure though.

(The only other quasi-stable neutral particles are neutrinos, and those are essentially non-interacting with any detector. They leave relativistically and you'll never see them again.)