Lack of gastric juice would cause multiple consequences. I'll describe three of them. Without the hydrochloric acid located in gastric juice, pepsinogen wouldn't be changed into pepsin in the stomach. Pepsin is an enzyme that digests proteins. The small intestine also digests proteins, so we would still get nourishment from them without pepsin. If the stomach digested no proteins at all, however, a doctor might suggest that a patient take supplemental enzymes to avoid malnutrition.
Another potential problem with achlorhydria (no stomach acid) is bacterial overgrowth in the stomach. Hydrochloric acid kills many of the dangerous bacteria that enter the digestive tract, so without the acid bacteria could multiply.
Gastric juice contains intrinsic factor as well as hydrochloric acid. The acid is required to separate vitamin B12 from food. Intrinsic factor is necessary for the absorption of vitamin B12 in the small intestine. Doctors can prescribe a way to overcome these problems if no gastric juice is made.