I made a cutting board for my self-healing cutting mat. Would I be able to use just the Minwax wood conditioner and no poly or stain? My first wood project was the craft table. After finishing it I used the wood conditioner with Polystain and didn't want to damage the surface with my rotary cutter, so I made a cutting board.
Yes you can apply it to your cutting board if you want to — what is sold variously as "wood conditioner", "pre-stain" and other names is merely a very dilute finish and as such can be used anywhere you feel something like that would be appropriate. So the real question then becomes why you want to, i.e. what purpose is it intended to have?
As it is such a dilute version of the original finish it serves little, if any, benefit beyond its original purpose.
And on a technical level you can leave the wood bare if you like, it'll work just fine and actually many 'utility surfaces' are best left bare. In woodworking workshops for example shooting boards, chopping hooks and other bench utilities, as well as many jigs, are regularly left as bare wood, as this gives greater grip on the wood being worked on them. And additionally a very light dampening of the surface can hugely increase the grip on the workpiece, if ever needed.
Unfinished wood does get grubby more easily (helping to prevent this is one of the primarily reasons we finish) but removing this sort of grubbiness is not terribly difficult if you ever find it unsightly, again bearing in mind it's a utility item so it doesn't have to be spotless.