Only parameters can be hidden unfortunately, and only one at a time. It could take an hour just to hide unwanted parameters for a single figure that has morphs loaded, but animating would be so much easier afterward. Selecting Show Hidden Parameters toggles them all back on globally, but also includes all the parameters hidden by default.

As far as I can tell you can't inadvertently keyframe a user-hidden parameter unless you apply Resample Keyframes, which means if you want to resample a single parameter of an element you can't do it by temporarily hiding the others–you still have to duplicate the figure or prop first, apply the resample, then copy the resampled keyframes back to the relevant parameter of the original figure or prop.

It would be so nice to be able to hide props, lights and cameras. Adding a toggle on the Hierarchy Editor so that anything made invisible there would also be hidden on the Animation Palette would make sense. That should be the default anyway. I can't think of a reason why I'd want to keyframe something when it's invisible.