Along my concrete block walls, I have 1/2" furring strips every 16",
then sheetrocks are attached to the furring strips. The furring
strips make it possible for 1/2" electrical conduits and copper pipes
to run across or up and down the walls.
In some cases I have 3/4" pipes or electrical conduits, so I go with
3/4" furring strips.
In some cases in a shower area, I have shower valves that sticks out
further and it needs 1.5" of space. Now, I can attach 2x2 or 2x4
turned on it's face to the concrete wall and furr it out this way. Or
may be at 1.5" I might as well build a real wall butt up against the
concrete wall, with it's own top and bottom plates.
At what depth do you think it crosses the threshold form using furring
strips to a real wall?

I would consider anything up to 1X material to be furring. Once I have
bought a 2x4, I might as well turn it on edge and use it as actual studs.
You'll have more room for pipes, wires, etc., and can add more insulation
if needed.

Also, I would be a little concerned about piercing wires and pipes run in a
3/4" or less furred space when hanging drywall, a picture, shelves, etc.
In a normal stud wall the wires/pipes are set back far enough that a 1-
1/2" screw wouldn't reach them, or you install metal protector plates if
they are close to the face of the stud. Just something to think about.

Anthony