Depends on the manufacturer. Each media formulation is different.
However, the purification process and the fermentation process would leave no trace amounts of soy or corn regardless of the media used. So when you say "soy or corn products/byproducts in any way, shape, or form ", I am not sure it applies in rennet manufacture using common biotechnological art.
I mean, when you manufacture soy peptone, for example, and then use that in the medium to ferment and produce chymosin from rhizomucor miehei, I don't see how that is a byproduct of soy.