Now as to the other point, that the objects of these Laws suffer voluntarily ... it supposes, what is false in fact, that it is in a man's moral power to change his religion whenever his convenience requires it. If he be beforehand satisfied that your opinion is better than his, he will voluntarily come over to you, and without compulsion; and then your Law would be unnecessary; but if he is not so convinced, he must know that it is his duty in this point to sacrifice his interest here to his opinion of his eternal happiness, else he could have in reality no religion at all. In the former case, therefore, as your Law would be unnecessary; in the latter, it would be persecuting; that is, it would put your penalty and his ideas of duty in the opposite scales; which is, or I know not what is, the precise idea of persecution.Reminds me of Godwin. It has the same concept of persuasion. Either I, in my own judgment, come to see your idea as best, and so compulsion is unnecessary, or I don't, in which case you can't reasonably expect me to change my mind. Godwin would say in the second case you should rethink whether you are correct if you can't be persuasive; Burke here says in the second case you can't say people are volunteering to suffer, because they'd suffer either way they chose.
The Great Melody by Conor Cruise O'Brien page 42 quoting Burke on why more Catholics didn't convert to Protestantism due to the Irish Penal Laws: