What, if any, were the Catholic orders that opposed the Catholic Inquisition? During the Inquisition of the Middle Ages, Dominicans and Franciscans were the main church inquisitors. I was wondering if there were other religious orders that, as a whole, opposed the Inquisition.  I am not interested in merely individuals within orders who objected, but rather groups as a whole that did so.

I have only found mention of an individual monastery in Spain (San Isidro del Campo), not of any religious orders.
Distinguo:

That Gregory IX, through his appointment of Dominicans and Franciscans as inquisitors, withdrew the suppression of heresy from the proper courts (i.e. from the bishops), is a reproach that in so general a form cannot be sustained. So little did he think of displacing episcopal authority that, on the contrary he provided explicitly that no inquisitional tribunal was to work anywhere without the diocesan bishop's co-operation.
Old Catholic Encyclopedia on Newadvent.org

I only throw this out there because of the popular support of the Inquisition would make it highly unlikely that orders were opposed to the Inquisition.
The other thing to distinguo is that the Dominicans and Franciscans were new orders, mendicant orders. Preachers and friars who went out to meet the people.  The other orders hung out in their monasteries.
I only mention these things to break down the two principles that form this question

That the Dominicans and Franciscans were the main church inquisitors.  They certainly had no power outside of the local bishop and were not independent of them when they were in his diocese.

That you can compare Dominicans and Franciscans to Benedictines.



However, the Catholic Encyclopedia says that St. Bernard of Clairvaux, who the Bernadines are named after, was opposed to the tactics of the inquisition.  However, I don't think the Bernadines were 'lead' by him, just formed in his honor.

Whether they be convicted of error, or freely confess their guilt, Catharists are not to be put to death, at least not when they refrain from armed assaults upon the Church.
ibid

so I think that doesn't jibe with your request that it not just be a person who took issue with the inquisition.  But he was a highly influential Cistercian - and apparently not rebuked for his stance; he was known for his preaching against the Cathars.