For one, consider that the Bible is not the clearest and most consistent guide. The Reformations happened after all because it is so easy to disagree about interpreting it, not only on the meaning of wording but how that wording is even translated at all. So the Bible does not make things clear and unanimous. Secondly, there was never a church doctrine against execution, the church was capable of encouraging it. So there was no real sense that execution was ever supposed to be out of line. and not many people in Early Modern Europe—if any— argued such a position let alone were heard.

However, it was recognised the Bible, particularly in the New Testament, does provide some encouragement for peace and love. William Warham, Archbishop of Canterbury, a councillor of the first Tudor Henry VII once preached a sermon in the early days of Henry VIII's reign arguing that war was not only costly and risky, but spiritually suspect as an act of great violence. Henry VII and his councillors did not oppose war all together, Henry VII made the traditional gestures of quarrelling with the French because the English were still salty about recently losing the Hundred Years War. But they did recognise peril in it, and it is interesting that the more sceptical critics of war in Henry VIII's time from his council were the bishops; Warham and Foxe. While many bishops, frequently political figures in local or national affairs, were accepting of war during the Medieval and Early Modern Period the spiritual argument for peace, as opposed to the spiritual argument of Holy War, was definitely raised by some.

And there were those who opposed or were uncomfortable with religious persecution during the Reformations. James VI and I said "I will never allow in my conscience,that the blood of any man shall be shed for the diversity of opinion in religion" although he did still support a moderate level of persecution.

The theological argument in favour of burning was threefold; firstly, that heretics commit a grievous crime against God, that they threaten the souls of others with the infection of their heresy, and that burning might simulate purgatory and therefore help their benighted soul gain redemption. On that last point, you can see why protestants weren't particularly enthusiastic about burning, although they did use it somewhat for general heresy, secular treason with hanging or hanging, drawing and quartering was preferred for Catholic recusants (and separatist Puritans). Burnings in England petered out in the 17th century.