Was Oliver Cromwell’s army fielded literally by the church? No. Were the papal armies? Yes.
It’s a distinction with a difference. Cromwell’s excesses were fuelled in part by widespread outrage over treatment of the Waldenses, he returned the atrocities in kind. Is this right, is it Christian? No, but words mean things and actions have consequences.
As a matter of fact Cromwell reported directly to the head of the Church of England.