Again, shoutout to @Fr_of_Jazz for this excellent response.
(4) The statement in question is from Exsurge Domine =ED], against the errors of Martin Luther, listing and rejecting 41 doctrinal and moral propositions asserted by Luther in the context of his works. It reads: “33. That heretics be burned is against the will of the Holy Spirit.”
(a) He denied the authority of a state to use capital punishment for heretics in the social, cultural, and political context of his times.
(i)The belief that the Church and political life were interlocked was presumed, accepted, and willed by the people. Heresy was, therefore, a crime against the civil government, treason.
(ii) Heretics weren’t just people who believed differently; but often had armies and political agendas that were seditious to the political order of the time.
(b) Luther had written: “To the Christian Nobility of the German Nation”
© ED rejects the assertion that capital punishment of heretics (under certain conditions in the context of the times) is against the will of God.
(d) (i) The method of burning at the stake was a common method of execution at the time. The emphasis is not on the method, which is entirely contingent.
(ii) The relationship of church and state juridically and in the minds of the people at the time is contingent.
(e) Leo X closes by saying that the propositions rejected are “either heretical, scandalous, false, offensive to pious ears or seductive of simple minds, and against Catholic truth.” Luther’s contingent political judgment while rejected at the time cannot be considered heretical. There is no language indicating Leo X is infallibly defining a dogmatic or moral teaching. It is also important to recall that in Protestant lands at the time likewise “heretics” were burned at the stake.
(f) Changes regarding the role of religion in the social order and consequently a clearer understanding of the right to freedom of the will from external constraint in religious matters makes it evident that heresy is not a capital offence.
(a) It is absurd in the extreme to think that the method (burning at the stake) was ever the issue. Denial of the right of the state at the time to use capital punishment to repel heresy was.
(b) As per (4)(f) above heresy is not now viewed as a capital offence.
© Capital punishment (for crimes other than heresy) is still not absolutely rejected in RC moral teaching although its use given the context of the times and the available means to protect society now is extremely limited. “Today however, as a result of steady improvements in the organization of the penal system, such cases [requiring capital punishment] are very rare, if not practically non-existent.” (Evangelium vitae, 56)
I hope this helps.