I’m sorry, but this wasn’t “principle in the Church’s social doctrine that says that the death penalty can only be applied when the criminal involved is so violent”. If you look at
this list, I think you’ll find few of them were violent.
Also, again from Aquinas:
*In obedience to Our Lord’s institution, the Church extends her charity to all, not only to friends, but also to foes who persecute her, according to Matthew 5:44: “Love your enemies; do good to them that hate you.” Now it is part of charity that we should both wish and work our neighbor’s good. Again, good is twofold: one is spiritual, namely the health of the soul, which good is chiefly the object of charity, since it is this chiefly that we should wish for one another. Consequently, from this point of view, heretics who return after falling no matter how often, are admitted by the Church to Penance whereby the way of salvation is opened to them.
The other good is that which charity considers secondarily, viz. temporal good, such as life of the body, worldly possessions, good repute, ecclesiastical or secular dignity, for we are not bound by charity to wish others this good, except in relation to the eternal salvation of them and of others. Hence if the presence of one of these goods in one individual might be an obstacle to eternal salvation in many, we are not bound out of charity to wish such a good to that person, rather should we desire him to be without it, both because eternal salvation takes precedence of temporal good, and because the good of the many is to be preferred to the good of one. Now if heretics were always received on their return, in order to save their lives and other temporal goods, this might be prejudicial to the salvation of others, both because they would infect others if they relapsed again, and because, if they escaped without punishment, others would feel more assured in lapsing into heresy. For it is written (Ecclesiastes 8:11): “For because sentence is not speedily pronounced against the evil, the children of men commit evils without any fear.”
For this reason the Church not only admits to Penance those who return from heresy for the first time, but also safeguards their lives, and sometimes by dispensation, restores them to the ecclesiastical dignities which they may have had before, should their conversion appear to be sincere: we read of this as having frequently been done for the good of peace. But when they fall again, after having been received, this seems to prove them to be inconstant in faith, wherefore when they return again, they are admitted to Penance, but are not delivered from the pain of death. *
Aquinas didn’t make this stuff up - he was justifying the regular practice of the Church as it existed in his time. Now, it is true that Mohammad lead many military campaigns during his life, and that war is more inherent to that religion. But unlike Islam, Christians have waged our share of Holy Wars* in spite of* what is contained in the teachings of Christ - so I think we have a lot more to answer for, since we should have known better.