This is exactly why I don't buy grated cheese. If I need it grated in quantity, I use a food processor. It's 'step one' if I'm making pesto - if that's you, too, and you're going to use the processor to make the entire batch, dump the grated cheese out before using it for the garlic, then add the pine nuts, the cheese you just grated with a bit of oil, then fresh basil. I use a processor for pesto as I make it by the quart (about a gallon per season). I often use Romano in place of Parmesan and sometimes use parsley along with basil, so it's arguably not 'Genovese' style but we like it.

At table, we use one of those hand-crank graters.

Interesting that so many other processed foods contain cellulose. I'm a little surprised that it wasn't the number one flour adulterant in Victorian England. Instead, it was chalk, then alum. Neither is good for you, and alum can cause brain damage if consumed chronically - but they both made for very white 'white' bread, which was a sign of bread purity in those times.

As far as tomato sauce containing cellulose, maybe I'm just not looking at the 'right' brands but I haven't noticed it on an ingredient list. I look at those carefully; anything with a sugar (dextrose, maltose, etc.) go back on the shelf.

Also, I've noticed that hand grated Parmesan and Romano do not melt as well as, say, cheddar or provolone; neither works all that well as a 'melty' cheese on pizza.