I take the approach where I move what I can move easily with plastic sliders.

As I do the room-by-room walk-through with the customer, I usually point to the furniture and say "I can move this, not move that", etc.

I rarely get a customer who objects. I had two different customers (usually when the man of the house hires me) a few weeks ago who wanted absolutely everything moved in all the rooms. Both stayed and helped me move the furniture without my asking, however.