I am almost 100% sure that furring strips are not structural.
For wight issue it all depends on the thickness and the material of the furring strip. You can use 1x2 furring strip or a 2x4 furring strip or sometimes a 1/2" plywood is being used as furring strip.
are you trying to hang a fixture OFF of a furring strip?
(B) Structural Mounting. An enclosure supported from a
structural member of a building or from grade shall be
rigidly supported either directly or by using a metal, polymeric,
or wood brace.
That's like saying "how much will my string hold?"
Not enough info. I agree with Edward, depends on what material/thickness the strips are and what you are wanting to mount to them.
If it's just a normal light no problem, 200# motor, maybe not.
Also depends on how well the strips are secured to the joists.