Can't select an object while in bone pose mode. (Lock object modes is off) As the title says. Lock object modes is off, but for some reason I still can't select the rigged character (or any other object) while in armature pose mode. Tried appending the whole thing into other project, it worked for some time, then started having the same problem. 

As a temporary work-around, I'm selecting object from the outliner. Obviously this is much less preferable than just being able to select them in the viewport window.
https://developer.blender.org/T65471
Short solution:
Press Alt+Z in Pose Mode, or uncheck &quot;Fade Geometry&quot; in overlays (both do the same).