Does anyone know what tool they use? I’ve tried with shears and knives, and it always looks like h*ll.
Power tools specially designed for the job.
Two pieces of metal clamp the rubber just to either side of the cut, and a really sharp bit slides between them to cut it.
It can do this hundreds of times a minute.
A sharp butcher’s knife will do a clean job if you drag it along the surface, rather than sawing with it. It helps if you can keep the foam being cut under a bit of tension.
An electric carving knife works well for softer foam, such as is used in upholstery.
I’ve audited a foam rubber packing company. Keeper is correct; they use large jigsaws, mostly, or very sharp knives. Depends on the specific peice and cut, but it’s all power tools.
Water jet machines are also well-suited for soft materials, and aren’t all that expensive. They also don’t have to be resharpened.
An added thought here. When I read the O.P., I thought that F.U. was referring to the custom-molded foam inserts that surround many items. In THAT case, rapidly expanding foam is jetted in against the plastic sheeting surrounding the item. It swells to fit the box, and protects the item.
I used FoamBoy just tonight. It’s a cheap electric knife. I’ve had it for about 17 years, and as long as you spritz a bit of WD-40 onto the blades now and again, it will slice through high-density closed cel urethane foam rubber quite nicely.
No, I won’t tell you what I was cutting !!! 
Cartooniverse
Water + foam rubber = soggy mess?
I just got rid of three giant foam cutting jigsaws in perfect shape for scrap. They cost hundreds of thousands to put in place about 15 years ago. The equipment broker had no use for them because the motors and thin, hihg speed blades were too lightweight to use for anything else. I think they are using water jets now for foam cutting.
Very thin stream of water at like 40,000psi, not a lot of water, just evil pressure. It also wont snag or scortch the material being cut like laser or mechanical cutting can.
Here’s one of the foam cutting machines I had to trash last week
Notice the thin blade and small motor.
The methods described here seem like they would make “straight” cuts. But I’ve seen some of “egg crate” foam rubber where you can’t even see the crack when the two pieces are put together. Any ideas on how these cuts are made? However it is done, it is good precision work.