The are few things in the dependency graph which lead to the issue:

• IDs are only built once.
• Object-data level (Armature, i,e,) builder dependent on the object visibility.

This caused issues when an armature is first built as not directly
visible (via driver, i.e.) and then was built as a directly visible.
This did not update visibility flag on the node for the custom shape
object.

The idea behind the fix is to go away form passing object visibility
flag to the geometry-level builders and instead rely on the common
visibility flush post-processing to make sure certain objects are
fully visible when needed.

This is the safest minimal part of the change for 3.0 release which
acts as an additional way to ensure visibility. This means that it
might not be a complete fix (if some configuration was overseen) but
it should not make currently working cases to not work.

The fix should also make modifiers used on rigify widgets to work.

The more complete fix will have is_object_visible argument removed
from the geometry-level builder functions.