• Character bone hierarchy has 2 selection sets stored, (bound to numeric keys), let's call them [S1] and [S2]
• [S1] is selectable, [S2] is not selectable
• Activating [S2] and then adding [S1] to it (using the Shift+numeric key) switches the selectable toggle on [S1], making it unselectable like [S2]

If this is a feature and not a bug, I can't figure out how it could be a useful one.

If within a bone hierarchy, part of the bones have Select toggle set to off, you select all bones in that hierarchy and switch visibility off and then on again, it makes the Select toggle off for all bones.

It seems any operation you do on a group of bones in which part of them have selectability turned off, that selectability set to off transfers to all the bones. This definitely looks like a bug to me.

Another example:

Select a group of bones in which part of them have selectability turned off. Set a key using any methods. Deselect. Now all bones have selectability turned off.