I started to wonder whether we missed the point entirely.

A quick scan of the internet yielded no comment from the artist himself, Andres Serrano, on "the point" of his photograph. A quick glance at some of his common subjects--such as bodily fluids and rotting corpses--indicate that the guy may just be a second-rate provocateur.

was it Christ's dignity that we were trying to protect, or was it the illusion of our own dignity?

I'm not quite getting your point. I mean, yes, Christ allowed himself to be humiliated for our sake, which had its purpose at that time and place. But he's no longer abasing himself by inhabiting human form. Anyway, if you'd like to elaborate, please do.