You should use the "Disable in viewports" icon : the one that looks like a monitor, not the one that looks like an eye.
It is a property of the object, and carries over when it's linked into another file, whereas the eye is a toggle specific to the current viewlayer. Since Since there can be many viewlayers with different values to this toggle in a given blender file, there is no telling which one to use when appending/linking.