While someone else might be able to chime in and provide a primary account of the public's perception. There is an important distinction as to how blinding and castrating became a practice in the first place.

For the first couple hundred years of the Empire's existence slitting someone's nose or ear was enough to keep them from having the right to ascend to the throne. This all changed with Justinian II. He was deposed in 695 and had his nose slit, only to return to the throne ten years later after a lengthy exile in Crimea.

His second reign didn't go any better, and Justinian was executed six years after coming to the throne in 711. This served to change how the aspect of physical disfigurement could block someone from ascending to the throne. Whereas before any disfigurement prevented you from being God's representative on Earth, Justinian proved that this was not enough. Thus, we see future Byzantine leaders going to much further lengths to prevent their enemies from gaining power. Because, if you don't have eyes or the ability to reproduce, what good are you?

Sorry I don't have a direct answer to your question. I would be interested to see a firsthand account of what the clergy or common folk thought of this practice. But from my experience they seemed to be largely ambivalent about it. Blinding and castration was usually punishment for treason, so I would be surprised if there was ever an account condemning it.

If no one else can provide an answer I can try and look in the footnotes of the three John Norwich books I have somewhere in my closet. However, I don't recall him mentioning the public's opinion on the matter.

Additionally, if anyone wants to research it on their own, here is a list of all the famous blind and castrated Byzantines: http://en.wikipedia.org/wiki/Political_mutilation_in_Byzantine_culture

I can't answer your actual question but would note that blinding dissuaded further treason while leaving the traitor time to repent his sin. Since treason was also sacrilege against the elect of God leaving him blind but alive in some monastery was considered merciful. As for punishing non political crimes, it was a rough world. Disfigurement from accident or disease were a much more common fact of life for the common farmer or laborer than now.I don't recall that castration was a common punishment though. In fact some parents saw it as a path to a secure future for a son. (As with castrati as singers until the 20th century.) I think that it is still debated whether castration after puberty precluded sexual enjoyment only short of ejaculation. I can say that the church has always opposed mutilation in theory, hence the opposition to surgery. On the other hand it was inherited from the ancient world which had no such quibbles. Long term imprisonment for crime (as opposed to politics) was not common which left only mutilation at either an extremity or the neck. If there is little evidence of opposition to corporal punishment that is probably because there was little and it was taken as having always been a fact of life, as it still is in some places. Life was tough, children were sold into slavery because they couldn't be fed, as they still are in some places. The life of an individual (much less a common criminal) just never mattered much before the modern world.