I have no problem carrying binoculars in a harness while using the gun bearer. My wife made the binoc harness for me - the harness closely resembles a FHF harness.
However, when using the gun bearer my rifle barrel sticks up very close to my face, so I have to be very careful when actively using binoculars. Don't want to smack my nice glass against the muzzle. It's possible I just need to adjust the gun bearer so the muzzle isn't so close to my face. Admittedly I haven't tried...
It's not typically an issue for me because I prefer to carry the rifle slung over my shoulder while actually hunting vs. hiking in to camp or packing a load of meat.