The challenge of this question is understanding what place torture has in the minds of the torturer, the tortured, the witnesses, or, put another way, what the function of torture is.

First, the place of the body in the medieval mind.

We can't assume that de-sensitization as we know it has always been an eternal emotional mode. Perhaps moderns have instead become sensitized to death in new ways. The objectification of death and pain have had different meanings over time; what you and I see - what we think when we see and feel - when we see blood and guts may not be what medievals saw (or to paraphrase /u/macoafi, does lifelong, intimate proximity to injury and death change what you see when you see the dead and their guts?). What is partible between the body, which is fleeting and temporary, and the soul?

For example, how do we know what to think about bodily torture if over 200 'heretics' are prepared to walk onto their own bonfire as they did at the siege of Montsegur March 16, 1244?

And here we can ask other questions:

1. what if we believe in truth, and that there are only limited ways to obtain truth?

2. what if we believe corporal punishment is effective?

3. what if we believe that the soteriological (saved) condition of the soul is what matters?

Then we might not see the matter of a medieval's witness to torture as one of becoming inured to violence, but in fact accepting a different purpose to, and different result of, violence.

Second, jurisdiction and meaning of torture.

This leads us to questions about the public function of torture and punishment. For the early middle ages, the ordeal was the preferred method of judgement: truth was discovered, quickly and without doubt.

For all their shortcomings, more clearly denounced throughout the twelfth century, the archaic procedures - oaths, ordeals, judicial combats - produced definitive decisions. [Peters, p45]

As Roman law began to make its reappearance in the 11th century, the older accusatorial procedures and the ordeal came under a challenge of the Roman-style inquest (quaestio). These placed priority on witness and testimony:

Paradoxically, even though the various forms of the inquest produced entirely new pictures of defendants, cases and witnesses, vastly more information than had ever surfaced in a routine trial, they also increased the fear of error. Confession, once only one of the several means of corroborating an accusation under older procedures, now loomed larger than ever as a means of overcoming that certainty [...] Faced with the prospect of open testimony challenged by the defendant, or with secret testimony doubted by the judge, and by a series of proofs that had yet to be graded in terms of reliability and trustworthiness, late twelfth- and thirteenth-century jurists and teachers of law raised the confession of the accused to the highest level of value [Peters, p46]

But the clearly developing importance of confession in lay law and within the Church created a fast-moving dynamic to fixing and obtaining confession as evidence in criminal matters. Torture, as means to confession-as-evidence, became the subject of ecclesiastic and secular jurists.

As torture was introduced into legal procedure proper, it had to take its place within the framework of confession and the law of evidence. Both ecclesiastical and lay law asserted, for example, that no confession could be extorted. Hence, torture was not a means of proof, but a means of obtaining a confession. It did not intend to force a guilty pleas, but a specific statement that contained details that 'none but the criminal could possibly know'. It could be expected to achieve these goals because of those events that triggered its use in the first place. First, there had to be at least one eyewitness or sufficient probable cause that the accused had committed the crime; the probable cause was measured by the number of specific indicia ranked and weighted according to accepted procedure. Second, when it was decided to apply torture, the court had to be reasonably convinced that a confession would be obtained. Third, the accused would be preached to and implored to make a confession, and to this end he was often shown the instruments of torture before the application itself [Peters, p50]

Moreover, it was viewed as progress in justice:

Compared to the older forms of procedure, the new inquisitorial process appeared far less repugnant to contemporaries than it may at first seem to us. It was certainly more professional. The inquisitorial procedure offered much that would seem familiar and acceptable to a modern litigant: the avoidance of rigid, excessively formalized, and ritually announced and answered charges; the open airing of testimony and the weighing of evidence from both parties; the presence of a trained judge who might also act equitably in weighing intangibles. [Peters, p51]

Outside of arguments about law, justice and rightness of judgement (whether ecclesiastical or secular) we don't find objections to torture, nor do we find defence of it. The questions of torture aren't moral, they are rightness and appropriateness for discovering truth.

There is no doubt that citizens complained about the unlawful torture of subjects, as I wrote regarding complaints against the medieval inquisition here. The inquisition throws the question of torture into high relief for us as it did the medievals. Many, even within the 13th c Church, complained about and argued against the inquisitors use of torture and punishment, of its Christian lawfulness. But they did so on the grounds the role of the Church, not on questioning the rightness of torture per se.

Further reading on the history of torture in the west:

• Edward Peters, Torture, (University of Pennsylvania Press, 1996)

And on the Christian inquisitorial justification of torture and corporal punishment:

• Christine Caldwell Ames, Righteous Persecution: Inquisition, Dominicans, and Christianity in the Middle Ages, (University of Pennsylvania Press, 2011)