Well the “that” could be that the friend’s comment was that the image was insulting to Catholics, or the “that” could be referring to the specific reaction. It basically needed some better comma usage because there is a difference between:

His reaction was, that the image was, insulting to the Catholic religion and blasphemous.

and

His reaction was that, the image, was insulting to the Catholic religion and blasphemous.

I guess the vagueness comes from the double “was” usage.