I think the answer to this question is given in the very next paragraph of Matthew. Jesus condemns those who pick and choose actions of faith according to their will, instead of embracing the totality of the Father’s will.
Mt 7:21-23 "Not every one who says to me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who does the will of my Father who is in heaven. On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’ And then will I declare to them, ‘I never knew you; depart from me, you evildoers.’ "
I would suggest that the ones who successfully drove out demons and did mighty works in His name had to have SOME degree of serious faith, otherwise their faith-actions would have been impossible. The Methodists you cite in your example are doing just that. Yet Jesus condemns them anyway, for choosing to act according to their will and not the Father’s.
For a modern parallel, I think of certain celebrated “TV preachers” who went down in flames due to scandal. We have serious reservations about their salvation. Yet, along the way they still led many people to Christ.
We can also look at the Gospel of John, where Jesus clarifies that to keep producing good fruit, we must keep our will connected to the Father’s will.
Jn 15:4-6 Abide in me, and I in you. As the branch cannot bear fruit by itself, unless it abides in the vine, neither can you, unless you abide in me. I am the vine, you are the branches. He who abides in me, and I in him, he it is that bears much fruit, for apart from me you can do nothing. If a man does not abide in me, he is cast forth as a branch and withers; and the branches are gathered, thrown into the fire and burned.