Q:

Does digestion require hydrochloric acid?

Would our digestion function any differently if we secreted something else, like sulfuric or nitric acid, instead? I'd assume an acidic environment may be required, but not sure if chloride is also required as well!
Perhaps we just use it out of convenience—e.g., presumably blood serum $$\left[\ce{SO4^2-}\right] + \left[\ce{NO3-}\right] \ll \left[\ce{Cl-}\right]$$ and channeling polyatomic ions across the membrane may be significantly more difficult than doing the same for chloride as well! 
*Edit: In fact, Wikipedia states

In the stomach, chief cells release pepsinogen. This zymogen is activated by hydrochloric acid (HCl), which is released from parietal cells in the stomach lining. The hormone gastrin and the vagus nerve trigger the release of both pepsinogen and HCl from the stomach lining when food is ingested. Hydrochloric acid creates an acidic environment, which allows pepsinogen to unfold and cleave itself in an autocatalytic fashion, thereby generating pepsin (the active form). Pepsin cleaves the 44 amino acids from pepsinogen to create more pepsin.

So, while maybe something like $\ce{H2SO4}$ or $\ce{HNO3}$ could work too, hydrochloric acid is just more convenient to use?

A:

Parietal cells use ion pumps to expel protons and chlorine ions into the lumen, which create the necessary acidic environment to denature pepsinogen into pepsin.
It is the low pH environment that reconfigures or denatures pepsinogen into pepsin. The acid used does not matter. For example, one experiment in classifying properties of pepsinogen used a 3.5 pH solution of 0.5 N sulfuric acid to activate pepsin.
We evolved stomachs with parietal cells that use an energetically expensive process to maintain the acidic gradient necessary for digestion and protection from pathogens. 
It may be that biochemical pathways to generate other acids did not evolve, because it is either energetically cheaper for these cells to make HCl, compared with other pathways that would generate other acids of sufficient strength; or the relevant chemical components involved are more abundant than others in what we eat and drink, and thus easier to make in quantities needed for digestion and defense. Chloride ions also serve a role in maintaining intra- and extracellular fluid pressure and thus play a larger part as electrolytes in the normal function of the body — they are available and cells use them.
But to answer your main question, an acidic environment activates pepsin, and it is not chemically necessary for this to be created by hydrochloric acid.

