Depending upon soil and or stain levels there are decent enough options for enzyme free products. Have had good success with Arm & Hammer "free and clear", All (ditto), and of course various commercial/industrial products in one's stash.
Taking a hint from "non-bio" laundry detergents sold in UK one will add bit of good activated oxygen bleach and perhaps some STPP to kick things up a little.
Forsaking enzymes one may need to resort to old school laundry methods. Rinsing and pre-treating certain stains before things go to wash, and or using higher wash water temps.
As one has frequently stated commercial laundries then nor today largely are bothered with using enzymes. Rather they stick to what they've done for ages; chemistry, high water temps and liberal use of bleach (chlorine, oxygen, peracetic acid..) will all get you there.